Contemporary Mathematics 1988; 730 pp; softcover Volume: 78 Reprint/Revision History: third printing 1998 ISBN10: 0821850881 ISBN13: 9780821850886 List Price: US$88 Member Price: US$70.40 Order Code: CONM/78
 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 AMSIMSSIAM 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 lowdimensional 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 twodimensional 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 pseudoAnosov homeomorphisms
 T. Kohno  Linear representations of braid groups and classical YangBaxter 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 selfenergy 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
