DIMACS Series in
Discrete Mathematics and Theoretical Computer Science

VOLUME Twenty Five
TITLE: "Geometric and Computational Perspectives on Infinite Groups"
EDITORS: Gilbert Baumslag, David Epstein, Robert Gilman, Hamish Short, Charles Sims
Published by the American Mathematical Society

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Some years ago Daniel Gorenstein, who at that time was Director of DIMACS, proposed that DIMACS and the Geometry Center cooperate in sponsoring a workshop on geometric group theory. Danny was aware of some exciting developments occurring in that area, in particular the introduction of automatic groups. As computation in both its theoretical and practical aspects was an important part of these developments, a workshop sponsored by DIMACS and the Geometry Center seemed appropriate. The eventual result was two related workshops each taking advantage of the strengths of its host institution. This book is the prodeedings of those workshops.

The first workshop was held in January 1994 at the Geometry Center, and the second one the following March at DIMACS. The Geometry Center workhop focused on problems of practical computation and aimed at encouraging informal interaction among the participants. There were no formal lectures. The DIMACS workshop had a broader view and was organized more conventionally. The staffs at both places were helpful and effective. The workshops were supported by grants from DIMACS and the Geometry Center, and by an additonal grant from the National Science Foundation.

The developments in geometric group theory alluded to above involve new connections between geometry, computer science, and group theory. This kind of interpaly is evident in the articles included in this book. They are evidence of the reimagining of combinatorial group theory now in progress.

The Editors


Foreward ix
Preface xi
The Geometry Center Workshop xiii
The DIMACS Workshop xiv
Lower bounds of isoperimetric functions for nilpotent groups

    Jose Burillo

A filtration of the chain complex of a rewriting system

    Lisa J. Carbone

Formal languages and infinite groups

    Robert H. Gilman

Groups of deficiency zero

    George Havas, M.F. Newman, E.A. O'Brien

The Warwick automatic groups software

    Derek F. Holt

Some remarks on one-relator free products with amalgamation

    Arya Juhasz

Detecting quasiconvexity: Algorithmic aspects

    Ilya Kapovich

A user's quide to the mapping class group: Once punctured surfaces

    Lee Mosher

Computing nilpotent quotients of finitely

    Werner Nickel

An algorithm detecting hyperbolicity

    P. Papasoglu

On the finite subgroups of a context-free group

    Geraud Senizergues


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Document last modified on October 28, 1998.