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Braid Groups

Author: Vladimir Turaev; Christian Kassel
Publisher: New York, NY : Springer-Verlag New York, 2008.
Series: Graduate texts in mathematics, 247.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Vladimir Turaev; Christian Kassel
ISBN: 9780387685489 0387685480
OCLC Number: 318867408
Description: 1 online resource (: v.: digital.
Contents: 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 --
Appendix A. Presentations of SL2(Z) and PSL2(Z) --
Appendix B. Fibrations and Homotopy Sequences --
Appendix C. The Birman-Murakami-Wenzl Algebras --
Appendix D. Left Self-Distributive Sets --
References --
Index.
Series Title: Graduate texts in mathematics, 247.
Responsibility: by Vladimir Turaev, Christian Kassel.

Abstract:

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.

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