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＜電子ブック＞
Braid Groups / by Christian Kassel, Vladimir Turaev
(Graduate Texts in Mathematics. ISSN:21975612 ; 247)

版	1st ed. 2008.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2008
本文言語	英語
大きさ	X, 338 p. 60 illus : online resource
著者標目	*Kassel, Christian author Turaev, Vladimir author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Manifolds (Mathematics) LCSH:Algebra LCSH:Algebraic topology FREE:Group Theory and Generalizations FREE:Manifolds and Cell Complexes FREE:Order, Lattices, Ordered Algebraic Structures FREE:Algebraic Topology
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/978-0-387-68548-9

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