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Viser: Braid Groups
Braid Groups
Christian Kassel, Vladimir Turaev og O. Dodane
(2008)
Sprog: Engelsk
Springer New York
1.015,00 kr.
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Detaljer om varen
- 1. Udgave
- Hardback: 320 sider
- Udgiver: Springer New York (August 2008)
- Forfattere: Christian Kassel, Vladimir Turaev og O. Dodane
- ISBN: 9780387338415
* Introduces the theory of braids and braid groups
* Discusses recent developments in the field dealing with the linearity and orderability of braid groups
* Excellent presentation
* Includes numerous problems and examples
* Includes five appendices with other relevant material
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 SL(Z) and PSL(Z).- Fibrations and Homotopy Sequences.- The Birman Murakami Wenzl Algebras.- Left Self-Distributive Sets.
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