Braids, Links, and Mapping Class Groups. (AM-82), Volume 82 / Joan S. Birman.

Format:

Book

Author/Creator:

Birman, Joan S., author.

Series:

Annals of mathematics studies ; no. 82.

Annals of Mathematics Studies ; 238

Language:

English

Subjects (All):

Braid theory.

Knot theory.

Representations of groups.

Physical Description:

1 online resource (241 pages) : illustrations.

Place of Publication:

Princeton, NJ : Princeton University Press, [2016]

Language Note:

English

Summary:

The central theme of this study is Artin's braid group and the many ways that the notion of a braid has proved to be important in low-dimensional topology.In Chapter 1 the author is concerned with the concept of a braid as a group of motions of points in a manifold. She studies structural and algebraic properties of the braid groups of two manifolds, and derives systems of defining relations for the braid groups of the plane and sphere. In Chapter 2 she focuses on the connections between the classical braid group and the classical knot problem. After reviewing basic results she proceeds to an exploration of some possible implications of the Garside and Markov theorems.Chapter 3 offers discussion of matrix representations of the free group and of subgroups of the automorphism group of the free group. These ideas come to a focus in the difficult open question of whether Burau's matrix representation of the braid group is faithful. Chapter 4 is a broad view of recent results on the connections between braid groups and mapping class groups of surfaces. Chapter 5 contains a brief discussion of the theory of "plats." Research problems are included in an appendix.

Contents:

Frontmatter

PREFACE

TABLE OF CONTENTS

CHAPTER 1. BRAID GROUPS

CHAPTER 2. BRAIDS AND LINKS

CHAPTER 3. MAGNUS REPRESENTATIONS

CHAPTER 4. MAPPING CLASS GROUPS

CHAPTER 5. PLATS AND LINKS

APPENDIX: RESEARCH PROBLEMS

BIBLIOGRAPHY

INDEX

Backmatter

Notes:

Includes index.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (publisher's Web site, viewed 08. Jul 2019)

ISBN:

9781400881420

1400881420

OCLC:

979633634