Preface Over the last several years application of ideas from topology and computer science has led to a number of new developments in combinatorial group theory. These developments are referred to collectively as geometric group theory. The best known of them are related to automatic and word hyperbolic groups, but there are also independent lines of research originating in the theory of automata and formal languages. This volume consists of contributions by speakers at the 1998 AMS-IMS-SIAM Joint Summer Research Conference on Geometric Group Theory and Computer Sci- ence. The conference was organized by Gilbert Baumslag, Martin Bridson, James Cannon, Robert Gilman, and Michael Shapiro and held from July 5 to July 9, 1998 at Mount Holyoke College. The conference was devoted to computer theoretic aspects of geometric group theory and related areas. This theme is reflected in the number of decision prob- lems, complexity problems, insights gained from computer experimentation, and applications of formal language theory which occur in the following articles but the reader will see that geometry also plays a significant role. We hope that this book will facilitate further progress in an interesting new area of research. Robert Gilman ix
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