The Calculus of Braids by Patrick Dehornoy
Everyone knows what braids are, whether they be made of hair, knitting wool, or electrical cables. However, it is not so evident that we can construct a theory about them, i.e. to elaborate a coherent and mathematically interesting corpus of results concerning them. This book demonstrates that there is a resoundingly positive response to this question: braids are fascinating objects, with a variety of rich mathematical properties and potential applications. A special emphasis is placed on the algorithmic aspects and on what can be called the 'calculus of braids', in particular the problem of isotopy. Prerequisites are kept to a minimum, with most results being established from scratch. An appendix at the end of each chapter gives a detailed introduction to the more advanced notions required, including monoids and group presentations. Also included is a range of carefully selected exercises to help the reader test their knowledge, with solutions available.-
Hyperbolic Geometry from a Local Viewpoint
-
Undergraduate Algebraic Geometry
-
The Prime Number Theorem
-
Elements of the Representation Theory of Associative Algebras: Volume 2, Tubes and Concealed Algebras of Euclidean type
-
Notes on Hamiltonian Dynamical Systems
-
LMSST: 24 Lectures on Elliptic Curves
-
A Brief Guide to Algebraic Number Theory
-
Designs, Graphs, Codes and their Links
-
Logic, Induction and Sets
-
Fourier Analysis on Finite Groups and Applications
-
Introduction to Combinators and (lambda) Calculus
-
Representation Theorems in Hardy Spaces
-
Introduction to Approximate Groups
-
The Block Theory of Finite Group Algebras
-
Hyperbolic Geometry
-
Random Graphs, Geometry and Asymptotic Structure
-
Undergraduate Commutative Algebra
- Nearly Invariant Subspaces and their Applications
-
Celestial Mechanics
-
Sets and Transfinite Algebra
-
The Shrikhande Graph
-
Topics in Cyclic Theory
-
An Introduction to the Theory of Graph Spectra
-
Clifford Algebras: An Introduction
-
The Riemann Hypothesis for Function Fields
-
Introduction to Banach Algebras, Operators, and Harmonic Analysis
-
Fast Track to Forcing
-
The Block Theory of Finite Group Algebras: Volume 1
-
Computational Algebraic Geometry
-
Lectures on Kahler Geometry
-
Fourier Analysis: Volume 1, Theory
-
Semigroups of Linear Operators
-
An Introduction to Noncommutative Noetherian Rings
-
A Gentle Introduction to Homological Mirror Symmetry
-
Set Theory
-
Tensor Products of C*-Algebras and Operator Spaces
-
Introductory Lectures on Rings and Modules
'This book is a very clear introduction to the theory of braids, addressed to beginnersThe author has made a great effort to render the exposition in this book pleasant and interesting and to make the proofs complete. This book is probably the best first introduction to the theory of braids.' Athanase Papadopoulos, zbMATH
'… this text is an excellent reference for graduate students and researchers. It is great to have a single, comprehensive resource addressing the braid isotopy problem using so many different approaches. The definitions are thoughtfully constructed and proofs are very thorough and detailed.' Katherine Vance, MAA Reviews
'… this text is an excellent reference for graduate students and researchers. It is great to have a single, comprehensive resource addressing the braid isotopy problem using so many different approaches. The definitions are thoughtfully constructed and proofs are very thorough and detailed.' Katherine Vance, MAA Reviews
Patrick Dehornoy (1952–2019) was Professor Emeritus at Université Caen Normandie, and Senior Member Emeritus of the Institut Universitaire de France. His research focused on set theory, algebra, and topology in small dimensions. He authored close to 100 research articles and eight books.
| SKU | Unavailable |
| ISBN 13 | 9781108925860 |
| ISBN 10 | 1108925863 |
| Title | The Calculus of Braids |
| Author | Patrick Dehornoy |
| Series | London Mathematical Society Student Texts |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Cambridge University Press |
| Year published | 2021-09-09 |
| Number of pages | 220 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |