Braid groups

Braids and braid groups, the focus of this text, have been at the heart of important mathematical developments over the last two decades. Their associationwith permutations has led to their presence in a number of mathematical fields and physics. As central objects in knot theory and 3-dimensional topology, braid groups has led to the creation of a new field called quantum topology. Inthis well-written presentation, motivated by numberous examples and problems,the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence. This is followed by a treatment of the relationship between braids, knots and links. Important results then treat the linearity and orderability of the subject. Relevant additional material is included in five large appendices. Braid Groups will serve graduate students and a number of mathematicians coming from diverse disciplines. 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 INDICE: Braids and Braid Groups.- Braids, Knots, and Links.- Burau Representation.- Garside Monoids and Braid Monoids.- Representations and the Iwahori-Hecke Algebras.- Orderings.- Appendix A. Free Groups and Magnus Expansion.- Appendix B. Fibrations and Homotopy Sequences.- Appendix C. The Symmetric Groups.- Appendix D. Representations of Finite Groups and Finite-dimensional Algebras.- Appendix E. Presentations of the Modular Group.- Notes.- Bibliography.- Index

• ISBN: 978-0-387-33841-5
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 340
• Fecha Publicación: 01/07/2008
• Nº Volúmenes: 1
• Idioma: Inglés