Braid Groups

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 relatio...

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Bibliographic Details
Main Authors: Kassel, Christian, Turaev, Vladimir (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 2008, 2008
Edition:1st ed. 2008
Series:Graduate Texts in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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505 0 |a Braids and Braid Groups -- Braids, Knots, and Links -- Homological Representations of the Braid Groups -- Symmetric Groups and Iwahori#x2013;Hecke Algebras -- Representations of the Iwahori#x2013;Hecke Algebras -- Garside Monoids and Braid Monoids -- An Order on the Braid Groups -- Presentations of SL(Z) and PSL(Z) -- Fibrations and Homotopy Sequences -- The Birman#x2013;Murakami#x2013;Wenzl Algebras -- Left Self-Distributive Sets 
653 |a Complex manifolds 
653 |a Group theory 
653 |a Order, Lattices, Ordered Algebraic Structures 
653 |a Manifolds and Cell Complexes (incl. Diff.Topology) 
653 |a Algebraic Topology 
653 |a Algebra 
653 |a Group Theory and Generalizations 
653 |a Algebraic topology 
653 |a Manifolds (Mathematics) 
653 |a Ordered algebraic structures 
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520 |a 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