Braid Groups

Beschreibung

Braids and braid groups have been at the heart of mathematical development over the last two decades. Braids play an important role in diverse areas of mathematics and theoretical physics. The special beauty of the theory of braids stems from their attractive geometric nature and their close relations to other fundamental geometric objects, such as knots, links, mapping class groups of surfaces, and configuration spaces.

In this presentation the authors thoroughly examine various aspects of the theory of braids, starting from basic definitions and then moving to more recent results. The advanced topics cover the Burau and the Lawrence--Krammer--Bigelow representations of the braid groups, the Alexander--Conway and Jones link polynomials, connections with the representation theory of the Iwahori--Hecke algebras, and the Garside structure and orderability of the braid groups.

This book will serve graduate students, mathematicians, and theoretical physicists interested in low-dimensional topology and its connections with representation theory.

Braids and braid groups form central objects in knot theory and three-dimensional topology. They have also been at the heart of important mathematical developments over the last two decades. This introductory text presents the theory of braids and braid groups to the reader along with the recent developments in this field. Developments related to the linearity and orderability of braid groups are carefully presented. This well-written text is ideal for graduate students and all mathematicians with an interest in braids and braid groups.

Autor*in

Christian Kassel

Themen in »Braid Groups«

Burau Garside Homotopy Iwahori-Hecke Markov Permutation Representation theory Theoretical physics algebra configuration spaces fibrations homeomorphisms of surfaces low-dimensional topology topology

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From the reviews:"Details on … braid groups are carefully provided by Kassel and Turaev’s text Braid Groups. … Braid Groups is very well written. The proofs are detailed, clear, and complete. ... The text is to be praised for its level of detail. … For people … who want to understand current research in braid group related areas, Braid Groups is an excellent, in fact indispensable, text." (Scott Taylor, The Mathematical Association of America, October, 2008)"This is a very useful, carefully written book that will bring the reader up to date with some of the recent important advances in the study of the braid groups and their generalizations. It continues the tradition of these high quality graduate texts in mathematics. The book could easily be used as a text for a year course on braid groups for graduate students, one advantage being that the chapters are largely independent of each other." (Stephen P. Humphries, Mathematical Reviews, Issue 2009 e)“This book is a comprehensive introduction to the theory of braid groups. Assuming only a basic knowledge of topology and algebra, it is intended mainly for graduate and postdoctoral students.” (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1208, 2011)“The book of Kassel and Turaev is a textbook … for graduate students and researchers. As such, it covers the basic material on braids, knots, and links … at a level which requires minimal background, yet moves rapidly to non-trivial topics. … It is a carefully planned and well-written book; the authors are true experts, and it fills a gap. … it will have many readers.” (Joan S. Birman, Bulletin of the American Mathematical Society, Vol. 48 (1), January, 2011)
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