Christian Kassel, Vladimir Turaev (auth.)0387338411, 9780387338415, 9780387685489
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.
Table of contents :
Front Matter….Pages i-x
Braids and Braid Groups….Pages 1-46
Braids, Knots, and Links….Pages 47-91
Homological Representations of the Braid Groups….Pages 93-150
Symmetric Groups and Iwahori–Hecke Algebras….Pages 151-193
Representations of the Iwahori–Hecke Algebras….Pages 195-237
Garside Monoids and Braid Monoids….Pages 239-272
An Order on the Braid Groups….Pages 273-309
Presentations of SL 2 (Z) and PSL 2 (Z)….Pages 311-314
Fibrations and Homotopy Sequences….Pages 315-316
The Birman–Murakami–Wenzl Algebras….Pages 317-319
Left Self-Distributive Sets….Pages 321-326
Back Matter….Pages 1-17
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