Topology and Combinatorial Group Theory: Proceedings of the Fall Foliage Topology Seminars held in New Hampshire 1986–1988

Iris Lee Anshel (auth.), Paul Latiolais (eds.)354052990X, 9783540529903, 038752990X

This book demonstrates the lively interaction between algebraic topology, very low dimensional topology and combinatorial group theory. Many of the ideas presented are still in their infancy, and it is hoped that the work here will spur others to new and exciting developments. Among the many techniques disussed are the use of obstruction groups to distinguish certain exact sequences and several graph theoretic techniques with applications to the theory of groups.

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Table of contents :
On two relator groups….Pages 1-21
When is the homotopy set [ X, Y ] infinite?….Pages 22-26
Local collapses for diagrammatic reducibility….Pages 27-38
Periodic knots and desuspensions of free involutions on spheres….Pages 39-47
The Tits conjecture and the five string braid group….Pages 48-51
The finite basis extension property and graph groups….Pages 52-58
Subgroup presentations without coset representatives….Pages 59-73
Fractal dimensions of limit sets of some Kleinian groups….Pages 74-80
Bounded cancellation of automorphisms of free products….Pages 81-89
A short topological proof of Cohn’s theorem….Pages 90-95
On the homotopy type of 2-complexes with a free product of cyclic groups as fundamental group….Pages 96-108
Bias ideals and obstructions to simple-homotopy equivalence….Pages 109-121
Embeddings of acyclic 2-complexes in S 4 with contractible complement….Pages 122-129
Fixed subsets of homomorphisms of free groups….Pages 130-147
Note on a conjecture of Stephen Halperin’s….Pages 148-163
On the rank, the deficiency and the homological dimension of groups: The computation of a lower bound via fox ideals….Pages 164-174
A reduced spherical diagram into a ribbon-disk complement and related examples….Pages 175-185
* – Groups, graphs, and bases….Pages 186-191
Some topological graph theory for topologists: A sampler of covering space constructions….Pages 192-207