{"title":"Hansjörg Geiges","description":null,"products":[{"product_id":"introduction-to-contact-topology-book-hansjrg-geiges-9780521865852","title":"An Introduction to Contact Topology","description":"This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51003271282961,"sku":"NIN9780521865852","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ GARDNERS","offer_id":51844978966801,"sku":"NGR9780521865852","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"GB \/ NEW \/ INGRAM","offer_id":52402743279889,"sku":"NLS9780521865852","price":0.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/B0077A5RYU.jpg?v=1751391547"},{"product_id":"geometry-of-celestial-mechanics-book-hansjrg-geiges-9781107564800","title":"The Geometry of Celestial Mechanics","description":"Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.","brand":"WoB","offers":[{"title":"US \/ NEW \/ INGRAM","offer_id":51019981062417,"sku":"NIN9781107564800","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":51065225380113,"sku":"GOR014166624","price":0.0,"currency_code":"GBP","in_stock":false},{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":51171976118545,"sku":"CIN1107564808VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1107564808.jpg?v=1751430871"},{"product_id":"geometry-of-celestial-mechanics-book-hansjrg-geiges-9781107125407","title":"The Geometry of Celestial Mechanics","description":"Celestial mechanics is the branch of mathematical astronomy devoted to studying the motions of celestial bodies subject to the Newtonian law of gravitation. This mathematical introductory textbook reveals that even the most basic question in celestial mechanics, the Kepler problem, leads to a cornucopia of geometric concepts: conformal and projective transformations, spherical and hyperbolic geometry, notions of curvature, and the topology of geodesic flows. For advanced undergraduate and beginning graduate students, this book explores the geometric concepts underlying celestial mechanics and is an ideal companion for introductory courses. The focus on the history of geometric ideas makes it perfect supplementary reading for students in elementary geometry and topology. Numerous exercises, historical notes and an extensive bibliography provide all the contextual information required to gain a solid grounding in celestial mechanics.","brand":"WoB","offers":[{"title":"- \/ - \/ -","offer_id":51020410749201,"sku":"","price":0.0,"currency_code":"GBP","in_stock":true},{"title":"US \/ NEW \/ INGRAM","offer_id":51020412748049,"sku":"NIN9781107125407","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/1107125405.jpg?v=1751143494"},{"product_id":"geometry-on-manifolds-book-hansjrg-geiges-9783032242341","title":"Geometry on Manifolds","description":"This first course on differential geometry includes not only Riemannian manifolds, but also symplectic and contact geometry. Rather than treating these three fields of geometry as separate subjects, this text emphasises common features by organising the material according to ideas and methods shared by the three fields.   Specifically, this text highlights how certain concepts, such as structure-preserving vector fields or variational characterisations of curves adapted to a given geometric structure, find their analogous expressions in the respective field of geometry. For example, Frobenius integrability, which is primarily relevant for contact geometry, is discussed together with the classification of flat Riemannian manifolds, which requires very similar arguments.   Another case in point is the discussion of transformation groups (isometries, symplectomorphisms, contactomorphisms) and the corresponding Lie algebras. Two equivalent ways to construct this Lie algebra structure are described: from the usual Lie bracket of vector fields on the manifold, restricted to the subalgebra of structure-preserving ones, or from the right-invariant vector fields on the transformation group.   This book also provides a concise introduction to manifolds, vector bundles, differential forms and tensors. As a result, it contains more material than can be covered in a single semester, and it is possible to teach various courses from it, depending on the background knowledge one may want to assume. Many examples and exercises are integrated into the richly illustrated text, making the book suitable for self-study.","brand":"WoB","offers":[{"title":"GB \/ NEW \/ GARDNERS","offer_id":53605835309329,"sku":"NGR9783032242341","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/9783032242341.jpg?v=1780007043"}],"url":"https:\/\/www.worldofbooks.com\/collections\/author-books-by-hansjrg-geiges.oembed","provider":"World of Books ","version":"1.0","type":"link"}