Quantum groups and knot invariants / Christian Kassel, Marc Rosso, Vladimir Turaev

Auteur principal : Kassel, Christian, 1951-, AuteurCo-auteur : Rosso, Marc, Auteur • Turaev, Vladimir, 1954-, AuteurType de document : MonographieCollection : Panoramas et synthèses, 5Langue : anglais.Pays: France.Éditeur : Paris : Société Mathématique de France, 1997Description : 1 vol. (VI-115 p.) : fig. ; 24 cmISBN: 2856290558.ISSN: 1272-3835.Bibliographie : Bibliogr. p. 106-111. Index.Sujet MSC : 17B37, Lie algebras and Lie superalgebras, Quantum groups (quantized enveloping algebras) and related deformations
57K10, Manifolds and cell complexes - Low-dimensional topology in specific dimensions, Knot theory
17-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to nonassociative rings and algebras
57-01, Introductory exposition (textbooks, tutorial papers, etc.) pertaining to manifolds and cell complexes
18M05, Monoidal categories and operads, Monoidal categories, symmetric monoidal categories
En-ligne : Sommaire
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Résumés en français, allemand et russe

Bibliogr. p. 106-111. Index

This survey is an introduction to quantum groups, braided categories, knots, three-manifolds and their invariants. The first two algebraic topics are intended as preparation for the last three topological topics. Of the book's nine chapters, the first four represent the algebraic side and the last five the topological side. Although it is concisely written, proofs are given. While only certain aspects of the algebraic aspects of quantum groups are given, namely those needed for the topological applications, the book could be used as a text for a course which intends to do the topological topics. There are examples and exercises, and some proofs would have to have details filled in by the instructor and students. For this purpose, and for a general reference on its topics, it seems an excellent source. (Zentralblatt)

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