Braids and Coverings: Selected Topics

Front Cover
Cambridge University Press, Dec 7, 1989 - Mathematics - 191 pages
0 Reviews
This book is based on a graduate course taught by the author at the University of Maryland. The lecture notes have been revised and augmented by examples. The first two chapters develop the elementary theory of Artin Braid groups, both geometrically and via homotopy theory, and discuss the link between knot theory and the combinatorics of braid groups through Markou's Theorem. The final two chapters give a detailed investigation of polynomial covering maps, which may be viewed as a homomorphism of the fundamental group of the base space into the Artin Braid group on n strings.
 

What people are saying - Write a review

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

Contents

Braids and Configuration Spaces
1
1 Geometric braids
2
2 Configuration spaces of ordered finite pointsets and their fibrations
9
3 The braid group as fundamental group of a configuration space
14
4 Artins presentation of the braid group
18
5 Representation of braids as automorphisms of free groups
25
6 The Dirac string problem
39
Exercises
46
3 Geometric characterizations of polynomial covering maps
91
4 Polynomial covering maps and homomorphisms into braid groups
97
5 Characteristic homomorphisms for finite covering mans
103
6 An algebraic classification of the polynomial covering maps
108
7 Embedding finite covering maps into bundles of manifolds
114
Exercises
118
Algebra and Topology of Weierstrass Polynomials
121
1 Complete solvability of equations defined by simple Weierstrass polynomials
123

Braids and Links
49
1 Constructing links from braids
50
2 Representing link types by closed braids A theorem of Alexander
55
3 Combinatorial equivalence of closed braids Markovs theorem
59
4 The group of a link
66
5 Plane projections and braid representations of links
73
Exercises
79
Polynomial Covering Maps
81
1 Weierstrass polynomials and the finite covering maps associated with them
82
2 The canonical nfold polynomial covering map
86
2 Primitives for extensions of rings of continuous functions
130
3 The characteristic algebra of a finite covering map
133
4 Weierstrass polynomials and characteristic algebras
139
5 Some applications of characteristic algebras
143
Exercises
151
A presentation of the abstract coloured braid group
153
Threading knot diagrams
171
Bibliography
185
Index to Chapters IIV and Appendix 1
189
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »