Braid Groups: 247 (Graduate Texts in Mathematics, 247) - Hardcover

Kassel, Christian; Turaev, Vladimir

Hardcover

ISBN 10: 0387338411 ISBN 13: 9780387338415

Publisher: Springer, 2008

Synopsis

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.

About this title

Review:

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)

“This book is a comprehensive introduction to the theory of braid groups. Assuming only a basic knowledge of topology and algebra, it is intended mainly for graduate and postdoctoral students.” (Hirokazu Nishimura, Zentralblatt MATH, Vol. 1208, 2011)

“The book of Kassel and Turaev is a textbook ... for graduate students and researchers. As such, it covers the basic material on braids, knots, and links ... at a level which requires minimal background, yet moves rapidly to non-trivial topics. ... It is a carefully planned and well-written book; the authors are true experts, and it fills a gap. ... it will have many readers.” (Joan S. Birman, Bulletin of the American Mathematical Society, Vol. 48 (1), January, 2011)

Synopsis:

Braids and braid groups have been at the heart of important mathematical developments over the last two decades. Introduced to the field of mathematics by Artin in the 1920's, their association with permutations has led to their presence in a number of mathematical fields and even physics. They form central objects in knot theory and three-dimensional topology and have led to the creation of a new field called quantum topology. Important results related to their linearity and orderability have fostered a lot of mathematical activity. Braids and braid groups form the central topic of this text. The authors begin with an introduction to the basic theory highlighting the several definitions of braid groups and showing their equivalence. The relationship between braids, knots and links is then investigated. Recent developments in this field follow next, with a focus on the linearity and orderability of braid groups. This excellent presentation is motivated by numerous examples and problems. Five elaborate appendices containing additional relevant material complete the text.

Based on lectures given by the authors at the Bourbaki Seminar and in a graduate course, this well-written book is ideal for graduate students and all mathematicians that would like to be introduced to the fascinating world of braids and braid groups.

About this edition

• Publisher: Springer
• Publication date: 2008
• ISBN 10: 0387338411
• ISBN 13: 9780387338415
• Binding: Hardcover
• Number of pages: 348