{"title":"Louis H Kauffman","description":null,"products":[{"product_id":"knots-and-physics-third-edition-book-louis-h-kauffman-9789810241117","title":"Knots And Physics (Third Edition)","description":"This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this third edition, a paper by the author entitled “Knot Theory and Functional Integration” has been added. This paper shows how the Kontsevich integral approach to the Vassiliev invariants is directly related to the perturbative expansion of Witten's functional integral. While the book supplies the background, this paper can be read independently as an introduction to quantum field theory and knot invariants and their relation to quantum gravity. As in the second edition, there is a selection of papers by the author at the end of the book. Numerous clarifying remarks have been added to the text.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50398315774225,"sku":"CIN9810241119VG","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52618386211089,"sku":"NLS9789810241117","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9810241119.jpg?v=1750840092"},{"product_id":"laws-of-form-spencer-brown-at-esalen-1973-book-louis-h-kauffman-9781788360289","title":"Laws of Form: Spencer-Brown at Esalen, 1973","description":"\u003cp\u003eThis Special Issue of Cybernetics and Human Knowing contains rare material related to G. Spencer-Brown's book Laws of Form and its contents.\u003c\/p\u003e \u003cp\u003eIn 1973 there was a conference at Big Sur at which Spencer-Brown discussed his calculus with a group of scientists. This was the AUM Conference at Esalen, and the scientists consisted in an assortment of remarkable individuals exploring the cutting edge of human consciousness and culture, including Alan Watts, Ram Dass, John Lilly, Heinz von Foerster, Kurt von Meier, and others. One of the participants, Walter Barney, has written about this conference and has long been a keeper of the transcripts of Spencer-Brown's talks. In this issue we print Barney's transcripts of the conference and an article by Walter Barney and Kurt von Meier reflecting on the AUM conference. The transcripts are a remarkable amalgam of the thinking of Spencer-Brown and the questions and comments of the participants in AUM. The transcripts carry the same lucidity that infuses Laws of Form.\u003c\/p\u003e \u003cp\u003eThe other articles in this issue include a paper on Flagg Resolution by James Flagg and Louis Kauffman, a paper on Paper Computers and the Emergence of Fermions by Louis Kauffman, and a Virtual Logic Column by Louis Kauffman that is a new take on the Barber paradox and the Russell Paradox, based on satire, mirrors, and the key observation of Douglas Harding that no person can (in the absence of mirrors) perceive his or her own head. There is an American Society for Cybernetics Column by Zane Gillespie about the structure of implausibility in music, art, and cybernetics.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51051424842001,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51051428315409,"sku":"NIN9781788360289","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1788360281.jpg?v=1751154044"},{"product_id":"laws-of-form-book-louis-h-kauffman-9781845409807","title":"Laws of Form","description":"\u003cp\u003eThis volume is a collection of articles on themes related to the book Laws of Form by George Spencer-Brown. Laws of Form was first published in 1969 and brings forth a new articulation of the foundations of thought. In Laws of Form we have a mathematical formalism based on one symbol and an approach to the question how the world would appear if a distinction could be drawn. Laws of Form does not answer the question how, given nothing as a beginning, a distinction can, indeed must, inevitably take place. This second question must, in its own structure, be left to each individual thinker. Nevertheless, Laws of Form, beautifully written and content free (form is emptiness, emptiness is form) is the most powerful mathematical text on the edge of nothing that has been produced since Euclid's Elements. These papers are a tribute to Spencer-Brown and his singular achievement.\u003c\/p\u003e","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51053548536081,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51053551157521,"sku":"NIN9781845409807","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51910241321233,"sku":"GOR014457378","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ GARDNERS","offer_id":52094387683601,"sku":"NGR9781845409807","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1845409809.jpg?v=1751314075"},{"product_id":"knots-and-physics-fourth-edition-book-louis-h-kauffman-9789814383011","title":"Knots And Physics (Fourth Edition)","description":"This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51066677854481,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51066680344849,"sku":"NIN9789814383011","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52679831421201,"sku":"NLS9789814383011","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9814383015.jpg?v=1751320045"},{"product_id":"knots-and-physics-book-louis-h-kauffman-9789810216566","title":"Knots And Physics","description":"In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51196630466833,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51196632367377,"sku":"NIN9789810216566","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52147992658193,"sku":"NLS9789810216566","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9810216564.jpg?v=1750872639"},{"product_id":"temperley-lieb-recoupling-theory-and-invariants-of-3-manifolds-book-louis-h-kauffman-9780691036403","title":"Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds","description":"This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants. Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold invariants. The methods in this book are based on a recoupling theory for the Temperley-Lieb algebra. This recoupling theory is a q-deformation of the SU(2) spin networks of Roger Penrose. The recoupling theory is developed in a purely combinatorial and elementary manner. Calculations are based on a reformulation of the Kirillov-Reshetikhin shadow world, leading to expressions for all the invariants in terms of state summations on 2-cell complexes. Extensive tables of the invariants are included. Manifolds in these tables are recognized by surgery presentations and by means of 3-gems (graph encoded 3-manifolds) in an approach pioneered by Sostenes Lins. The appendices include information about gems, examples of distinct manifolds with the same invariants, and applications to the Turaev-Viro invariant and to the Crane-Yetter invariant of 4-manifolds.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51804181102865,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ GOOD \/ SBYB","offer_id":51804181397777,"sku":"CIN0691036403G","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691036403.jpg?v=1752247479"},{"product_id":"knots-and-physics-book-louis-h-kauffman-9789810216580","title":"Knots And Physics","description":"In this second edition, the following recent papers have been added: Gauss Codes, Quantum Groups and Ribbon Hopf Algebras, Spin Networks, Topology and Discrete Physics, Link Polynomials and a Graphical Calculus and Knots Tangles and Electrical Networks. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52148883128593,"sku":"NLS9789810216580","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52763899691281,"sku":"NIN9789810216580","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789810216580.jpg?v=1757604972"},{"product_id":"knots-and-physics-fourth-edition-book-louis-h-kauffman-9789814383004","title":"Knots And Physics (Fourth Edition)","description":"This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52332991152401,"sku":"NLS9789814383004","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52996046323985,"sku":"NIN9789814383004","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789814383004.jpg?v=1758153341"},{"product_id":"scientific-essays-in-honor-of-h-pierre-noyes-on-the-occasion-of-his-90th-birthda-book-louis-h-kauffman-9789814579360","title":"Scientific Essays In Honor Of H Pierre Noyes On The Occasion Of His 90th Birthday","description":"This book is a Festschrift for the 90th birthday of the physicist Pierre Noyes. The book is a representative selection of papers on the topics that have been central to the meetings over the last three decades of ANPA, the Alternative Natural Philosophy Association. ANPA was founded by Pierre Noyes and his colleagues the philosopher-linguist-physicist Frederick Parker-Rhodes, the physicist Ted Bastin, and the mathematicians Clive Kilmister, John Amson.Many of the topics in the book center on the combinatorial hierarchy discovered by the originators of ANPA. Other topics explore geometrical, cosmological and biological aspects of those ideas, and foundational aspects related to discrete physics and emergent quantum mechanics.The book will be useful to readers interested in fundamental physics, and particularly to readers looking for new and important viewpoints in Science that contain the seeds of futurity.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52352627540241,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52352628261137,"sku":"NLS9789814579360","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789814579360.jpg?v=1758182129"},{"product_id":"knots-and-physics-book-louis-h-kauffman-9789810203436","title":"Knots And Physics","description":"This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward the knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related with and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics, knots in dynamical systems.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52617284583697,"sku":"NLS9789810203436","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789810203436.jpg?v=1761529838"},{"product_id":"knots-and-physics-book-louis-h-kauffman-9789810203443","title":"Knots And Physics","description":"This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward the knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related with and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics, knots in dynamical systems.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52618348691729,"sku":"NLS9789810203443","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789810203443.jpg?v=1761532884"},{"product_id":"knots-and-physics-third-edition-book-louis-h-kauffman-9789810241124","title":"Knots And Physics (Third Edition)","description":"This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas.The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part I is a set of lectures on various topics related to Part I. Part I includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems.In this third edition, a paper by the author entitled Knot Theory and Functional Integration has been added. This paper shows how the Kontsevich integral approach to the Vassiliev invariants is directly related to the perturbative expansion of Witten's functional integral. While the book supplies the background, this paper can be read independently as an introduction to quantum field theory and knot invariants and their relation to quantum gravity. As in the second edition, there is a selection of papers by the author at the end of the book. Numerous clarifying remarks have been added to the text.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52619005559057,"sku":"NLS9789810241124","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789810241124.jpg?v=1761534700"},{"product_id":"quantum-topology-book-louis-h-kauffman-9789810215446","title":"Quantum Topology","description":"Discusses topics in the field of quantum topology, including: knot theory, exotic spheres and global gravitational anomolies; construction of 4D topological quantum field theories; computing the arf invariants of links; and the Casson invariants for two-fold branched covers of links.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":52663527768337,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":52663528325393,"sku":"NLS9789810215446","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789810215446.jpg?v=1762272252"},{"product_id":"quantum-topology-book-louis-h-kauffman-9789810225759","title":"Quantum Topology","description":"This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984\/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52675641606417,"sku":"NLS9789810225759","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53010990596369,"sku":"NIN9789810225759","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789810225759.jpg?v=1762302370"},{"product_id":"introductory-lectures-on-knot-theory-selected-lectures-presented-at-the-advanced-book-louis-h-kauffman-9789814307994","title":"Introductory Lectures On Knot Theory: Selected Lectures Presented At The Advanced School And Conference On Knot Theory And Its Applications To Physics And Biology","description":"This volume consists primarily of survey papers that evolved from the lectures given in the school portion of the meeting and selected papers from the conference.Knot theory is a very special topological subject: the classification of embeddings of a circle or collection of circles into three-dimensional space. This is a classical topological problem and a special case of the general placement problem: Understanding the embeddings of a space X in another space Y. There have been exciting new developments in the area of knot theory and 3-manifold topology in the last 25 years. From the Jones, Homflypt and Kauffman polynomials, quantum invariants of 3-manifolds, through, Vassiliev invariants, topological quantum field theories, to relations with gauge theory type invariants in 4-dimensional topology.More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.It is a remarkable fact that knot theory, while very special in its problematic form, involves ideas and techniques that involve and inform much of mathematics and theoretical physics. The subject has significant applications and relations with biology, physics, combinatorics, algebra and the theory of computation. The summer school on which this book is based contained excellent lectures on the many aspects of applications of knot theory. This book gives an in-depth survey of the state of the art of present day knot theory and its applications.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52681102688529,"sku":"NLS9789814307994","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":53352897577233,"sku":"NIN9789814307994","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789814307994.jpg?v=1762314750"},{"product_id":"laws-of-form-a-fiftieth-anniversary-book-louis-h-kauffman-9789811247422","title":"Laws Of Form: A Fiftieth Anniversary","description":"Laws of Form is a seminal work in foundations of logic, mathematics and philosophy published by G Spencer-Brown in 1969. The book provides a new point of view on form and the role of distinction, markedness and the absence of distinction (the unmarked state) in the construction of any universe. A conference was held August 8-10, 2019 at the Old Library, Liverpool University, 19 Abercromby Square, L697ZN, UK to celebrate the 50th anniversary of the publication of Laws of Form and to remember George Spencer-Brown, its author. The book is a collection of papers introducing and extending Laws of Form written primarily by people who attended the conference in 2019.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ INGRAM","offer_id":52690098356497,"sku":"NLS9789811247422","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":52763931574545,"sku":"NIN9789811247422","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789811247422.jpg?v=1762336929"},{"product_id":"on-knots-book-louis-h-kauffman-9780691084350","title":"On Knots","description":"On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":52736553713937,"sku":"NIN9780691084350","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":53009636622609,"sku":"CIN0691084351VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9780691084350.jpg?v=1763408020"},{"product_id":"shape-and-energies-of-geometric-objects-book-louis-h-kauffman-9789819819454","title":"Shape And Energies Of Geometric Objects","description":"In this book, we study the shape of different geometric objects (curves, surfaces, and knots) through small deformation: infinitesimal bending. The shape of geometric objects is determined by their geometric curvature as well as curvature-based functionals, which are referred to as energies. Different kinds of curvatures, their properties, and their influence on shape and energy are discussed. For the investigation of shape and energy, we use our own software visualization tools.We aim to offer a mathematical way of considering shape. That is, all the geometrical information that is invariant to translations, rotations, and size changes. A more flexible definition of shape takes into consideration the fact that we often deal with deformable shapes in reality. By allowing also isometric (or near-isometric) deformations, such as infinitesimal bending, the intrinsic geometry of the object will stay the same, while sub-parts might be located at very different positions in space.A special part of the book presents the construction of examples of unknots, as well as knots that can resist simplification by energy gradient and force evolution methods in programming models.","brand":"WoB","offers":[{"title":"- \/ - \/ INTERNAL","offer_id":53218337980689,"sku":null,"price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ NEW \/ INGRAM","offer_id":53218338406673,"sku":"NLS9789819819454","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9789819819454.jpg?v=1772842692"}],"url":"https:\/\/www.worldofbooks.com\/en-gb\/collections\/author-books-by-louis-h-kauffman.oembed","provider":"World of Books ","version":"1.0","type":"link"}