Braids: (Contemporary Mathematics)

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