Kassel C., Turaev V. Braid Groups

Springer, 2008. — 349 p. — (Graduate Texts in Mathematics 247). — ISBN: 978-0-387-33841-5.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
Braids, Knots, and Links
Homological Representations of the Braid Groups
Symmetric Groups and Iwahori–Hecke Algebras
Representations of the Iwahori–Hecke Algebras
Garside Monoids and Braid Monoids
An Order on the Braid Groups
Presentations of SL2(Z) and PSL2(Z)
Fibrations and Homotopy Sequences
The Birman–Murakami–Wenzl Algebras
Left Self-Distributive Sets