Braid Groups, Softcover reprint of hardcover 1st ed. 2008
Graduate Texts in Mathematics Series, Vol. 247

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Language: English

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Braid groups previously published in hardcover (series: graduate texts in mathematics)
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Braid groups (Graduate texts in mathematics, Vol. 247)
Publication date:
338 p. · 15.5x23.5 cm · Hardback

Braids and braid groups, the focus of this text, have been at the heart of important mathematical developments over the last two decades. Their association with 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.

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.

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.

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.

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 Includes supplementary material: sn.pub/extras