Topology and Combinatorial Group Theory [electronic resource] : Proceedings of the Fall Foliage Topology Seminars held in New Hampshire 1986–1988 / edited by Paul Latiolais.

On two relator groups -- When is the homotopy set [X, Y] infinite? -- Local collapses for diagrammatic reducibility -- Periodic knots and desuspensions of free involutions on spheres -- The Tits conjecture and the five string braid group -- The finite basis extension property and graph groups -- Subgroup presentations without coset representatives -- Fractal dimensions of limit sets of some Kleinian groups -- Bounded cancellation of automorphisms of free products -- A short topological proof of Cohn's theorem -- On the homotopy type of 2-complexes with a free product of cyclic groups as fundamental group -- Bias ideals and obstructions to simple-homotopy equivalence -- Embeddings of acyclic 2-complexes in S 4 with contractible complement -- Fixed subsets of homomorphisms of free groups -- Note on a conjecture of Stephen Halperin's -- On the rank, the deficiency and the homological dimension of groups: The computation of a lower bound via fox ideals -- A reduced spherical diagram into a ribbon-disk complement and related examples -- * - Groups, graphs, and bases -- Some topological graph theory for topologists: A sampler of covering space constructions.

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.