Braid Groups

  • Christian Kassel
  • Vladimir Turaev
Part of the Graduate Texts in Mathematics book series (GTM, volume 247)

Table of contents

  1. Front Matter
    Pages i-x
  2. Christian Kassel, Vladimir Turaev
    Pages 1-46
  3. Christian Kassel, Vladimir Turaev
    Pages 47-91
  4. Christian Kassel, Vladimir Turaev
    Pages 93-150
  5. Christian Kassel, Vladimir Turaev
    Pages 151-193
  6. Christian Kassel, Vladimir Turaev
    Pages 195-237
  7. Christian Kassel, Vladimir Turaev
    Pages 239-272
  8. Christian Kassel, Vladimir Turaev
    Pages 273-309
  9. Christian Kassel, Vladimir Turaev
    Pages 311-314
  10. Christian Kassel, Vladimir Turaev
    Pages 315-316
  11. Christian Kassel, Vladimir Turaev
    Pages 317-319
  12. Christian Kassel, Vladimir Turaev
    Pages 321-326
  13. Back Matter
    Pages 1-17

About this book

Introduction

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.

Keywords

Burau Garside Homotopy Iwahori-Hecke Markov Permutation Representation theory Theoretical physics algebra configuration spaces fibrations homeomorphisms of surfaces low-dimensional topology topology

Authors and affiliations

  • Christian Kassel
    • 1
  • Vladimir Turaev
    • 2
  1. 1.Inst. Rech. Math. AvancéeUniv. Louis Pasteur et CNRSStrasbourg CXFrance
  2. 2.Dept. MathematicsIndiana UniversityBloomingtonU.S.A.

Bibliographic information

  • DOI https://doi.org/10.1007/978-0-387-68548-9
  • Copyright Information Springer Science+Business Media, LLC 2008
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-0-387-33841-5
  • Online ISBN 978-0-387-68548-9
  • Series Print ISSN 0072-5285
  • About this book