**Contemporary Mathematics**

Volume: 78;
1988;
730 pp;
Softcover

MSC: Primary 20;
Secondary 32; 57

Print ISBN: 978-0-8218-5088-6

Product Code: CONM/78

List Price: $93.00

Individual Member Price: $74.40

**Electronic ISBN: 978-0-8218-7666-4
Product Code: CONM/78.E**

List Price: $93.00

Individual Member Price: $74.40

# Braids

Share this page *Edited by *
*Joan S. Birman; Anatoly Libgober*

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

# Table of Contents

## Braids

- Contents xi12 free
- Organizing Committee xv16 free
- List of Participants xv16
- Introduction xxiii24 free
- A construction of integrable differential system associated with braid groups 136 free
- Mapping class groups of surfaces 1348
- Automorphic sets and braids and singularities 4580
- The operator algebras of the two dimensional Ising model 117152
- Artin's braid groups, classical homotopy theory, and sundry other curiosities 167202
- Classification of solvorbifolds in dimension three - I 207242
- Pure braid groups and products of free groups 217252
- Polynomial covering maps 229264
- Arithmetic analogues of braid groups and Galois representations 245280
- Application of braids to fixed points of surface maps 259294
- Statistical mechanics and the Jones polynomial 263298
- Hurwitz action and finite quotients of braid groups 299334
- Heights of simple loops and pseudo-Anosov homeomorphisms 327362
- Linear representations of braid groups and classical Yang-Baxter equations 339374
- A survey of Heeke algebras and the Artin braid groups 365400
- On divisibility properties of braids associated with algebraic curves 387422
- The panorama of polynomials for knots, links and skeins 399434
- The structure of deleted symmetric products 415450
- Braid group technique in complex geometry, I: Linearrangements in Cp2 425460
- Problems 557592
- Polynomials from braids 575610
- The Jones polynomial of satellite links about mutants 587622
- On the deformation of certain type of algebraic varieties 593628
- Braids and discriminants 605640
- tk moves on links 615650
- Mutually braided open books and new invariants of fibered links 657692
- Generalized braid groups and self-energy Feynman integrals 675710
- Markov classes in certain finite symplectic representations of braid groups 687722
- The braid index of an algebraic link 697732
- Markov algebras 705740