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Kassel, Christian; Turaev, Vladimir

Braid Groups (Kartoniert / Broschiert / Paperback)

Springer New York, November 2010

Softcover reprint of hardcover 1st ed. 2008 - 356 S. - Sprache: Englisch - 238x157x23 mm Previously published in hardcover

ISBN: 1441922202 EAN: 9781441922205

In this well-written presentation, motivated by numerous 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.

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Braids and braid groups form central objects in knot theory and three-dimensional topology. They have also been at the heart of important mathematical developments over the last two decades. This introductory text presents the theory of braids and braid groups to the reader along with the recent developments in this field. Developments related to the linearity and orderability of braid groups are carefully presented. This well-written text is ideal for graduate students and all mathematicians with an interest in braids and braid groups.


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

Über den Autor

Dr. Christian Kassel is the director of CNRS (Centre National de la Recherche Scientifique in France), was the director of l'Institut de Recherche Mathematique Avancee from 2000 to 2004, and is an editor for the Journal of Pure and Applied Algebra. Kassel has numerous publications, including the book Quantum Groups in the Springer Gradate Texts in Mathematics series. Dr. Vladimir Turaev was also a professor at the CNRS and is currently at Indiana University in the Department of Mathematics.


From the reviews: "Details on ... braid groups are carefully provided by Kassel and Turaev's text Braid Groups. ... Braid Groups is very well written. The proofs are detailed, clear, and complete. ... The text is to be praised for its level of detail. ... For people ... who want to understand current research in braid group related areas, Braid Groups is an excellent, in fact indispensable, text." (Scott Taylor, The Mathematical Association of America, October, 2008) "This is a very useful, carefully written book that will bring the reader up to date with some of the recent important advances in the study of the braid groups and their generalizations. It continues the tradition of these high quality graduate texts in mathematics. The book could easily be used as a text for a year course on braid groups for graduate students, one advantage being that the chapters are largely independent of each other." (Stephen P. Humphries, Mathematical Reviews, Issue 2009 e)

ISBN 1-441922-20-2, ISBN 1-44-192220-2, ISBN 1-44192-220-2, ISBN 1-441-92220-2, ISBN 1-4419-2220-2

ISBN 978-1-441922-20-5, ISBN 978-1-44-192220-5, ISBN 978-1-44192-220-5, ISBN 978-1-441-92220-5, ISBN 978-1-4419-2220-5

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