Geometric group theory : proceedings of the Symposium held in Sussex, 1991. Vol. 1

These two volumes contain survey papers given at the 1991 international symposium on geometric group theory, and they represent some of the latest thinking in this area. Many of the world's leading figures in this field attended the conference, and their contributions cover a wide diversity of topics. Volume I contains reviews of such subjects as isoperimetric and isodiametric functions, geometric invariants of a groups, Brick's quasi-simple filtrations for groups and 3-manifolds, string rewriting, and algebraic proof of the torus theorem, the classification of groups acting freely on R-trees, and much more. Volume II consists solely of a ground breaking paper by M. Gromov on finitely generated groups. Cover......Page 1 Title......Page 4 Copyright......Page 5 Table of Contents......Page 6 Preface......Page 8 List of Participants......Page 10 Group Actions and Riemann Surfaces......Page 12 The Virtual Cohomological Dimension of Coxeter Groups......Page 30 The Geometric Invariants of a Group..A Survey with Emphasis on the Homotopical Approach......Page 35 String Rewriting - A Survey for Group Theorists......Page 48 One Relator Products and High-Powered Relators......Page 59 An Inaccessible Group......Page 86 Isoperimetric and Isodiametric Functions of Finite Presentations......Page 90 On Hibert's Metric for Simplices......Page 108 Software for Automatic Groups, Isomorphism Testing and Finitely Presented Groups......Page 131 Proving Certain Groups Infinite......Page 137 Some Applications of Small Cancellation Theory to One-Relator Groups and One-Relator Products......Page 143 A Group Theoretic Proof of the Torus Theorem......Page 149 N-Torsion and Applications......Page 170 Surface Groups and Quasi-Convexity......Page 180 Constructing Group Actions on Trees......Page 187 Brick's Quasi Simple Filtrations and 3-Manifolds......Page 199 A Note on Accessibility......Page 215 Geometric Group Theory 1991 Problem List......Page 219 The articles in these two volumes arose from papers given at the 1991 International Symposium on Geometric Group Theory, and they represent some of the latest thinking in this area. This first volume contains contributions from many of the world's leading figures in this field, and their contributions demonstrate the many interesting facets of geometrical group theory. For anyone whose interest lies in the interplay between groups and geometry, these books will be an essential addition to their library. v. 1. [Proceedings] v. 2. Asymptotic invariants of infinite groups / M. Gromov We begin by considering two familiar ways of constructing Riemann surfaces.