Braids, Links, and Mapping Class Groups

Front Cover
Princeton University Press, 1975 - Mathematics - 228 pages
1 Review

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.

 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

BRAID GROUPS
3
BRAIDS AND LINKS
37
MAGNUS REPRESENTATIONS
102
PROOF OF THEOREM 2 10
144
PLATS AND LINKS
192
RESEARCH PROBLEMS
216
INDEX
227
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

Bibliographic information