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Edited by: Joan S. Birman and Anatoly Libgober

Contemporary Mathematics
1988; 730 pp; softcover
Volume: 78
Reprint/Revision History:
third printing 1998
ISBN-10: 0-8218-5088-1
ISBN-13: 978-0-8218-5088-6
List Price: US$88
Member Price: US$70.40
Order Code: CONM/78
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Artin introduced braid groups into mathematical literature in 1925. In the years since, and particularly in the last five to ten years, braid groups have played diverse and unexpected roles in widely different areas of mathematics, including knot theory, homotopy theory, singularity theory, and dynamical systems. Most recently, the area of operator algebras has brought striking new applications to knots and links.

This volume contains the proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group, held at the University of California, Santa Cruz, in July 1986. This interdisciplinary conference brought together leading specialists in diverse areas of mathematics to discuss their discoveries and to exchange ideas and problems concerning this important and fundamental group. Because the proceedings present a mix of expository articles and new research, this volume will be of interest to graduate students and researchers who wish to learn more about braids, as well as more experienced workers in this area. The required background includes the basics of knot theory, group theory, and low-dimensional topology.

Table of Contents

  • K. Aomoto -- A construction of integrable differential system associated with braid groups
  • J. S. Birman -- Mapping class groups of surfaces
  • E. Brieskorn -- Automorphic sets and braids and singularities
  • A. L. Carey and D. E. Evans -- The operator algebras of the two-dimensional Ising model
  • F. R. Cohen -- Artin's braid groups, classical homotopy theory, and sundry other curiosities
  • W. D. Dunbar -- Classification of solvorbifolds in dimension three, I
  • M. Falk and R. Randell -- Pure braid groups and products of free groups
  • L. V.Hansen -- Polynomial covering maps
  • Y. Ihara -- Arithmetic analogues of braid groups and Galois representations
  • B. Jiang -- Application of braids to fixed points of surface maps
  • L. H. Kauffman -- Statistical mechanics and the Jones polynomial
  • P. Kluitmann -- Hurwitz action and finite quotients of braid groups
  • T. Kobayashi -- Heights of simple loops and pseudo-Anosov homeomorphisms
  • T. Kohno -- Linear representations of braid groups and classical Yang-Baxter equations
  • G. I. Lehrer -- A survey of Hecke algebras and the Artin braid groups
  • A. Libgober -- On divisibility properties of braids associated with algebraic curves
  • W. B. R. Lickorish -- The panorama of polynomials for knots, links, and skeins
  • R. J. Milgram and P. Löffler -- The structure of deleted symmetric products
  • B. Moishezon and M. Teicher -- Braid group technique in complex geometry, I: Line arrangements in \(CP^2\)
  • H. R. Morton -- Problems
  • H. R. Morton -- Polynomials from braids
  • H. R. Morton and P. Traczyk -- The Jones polynomial of satellite links around mutants
  • M. Oka -- On the deformation of certain type of algebraic varieties
  • P. Orlik and L. Solomon -- Braids and discriminants
  • J. H. Przytycki -- \(t_k\) moves on links
  • L. Rudolph -- Mutually braided open books and new invariants of fibered links
  • M. Salvetti -- Generalized braid groups and self-energy Feynman integrals
  • B. Wajnryb -- Markov classes in certain finite symplectic representations of braid groups
  • R. F. Williams -- The braid index of an algebraic link
  • D. N. Yetter -- Markov algebras
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