Geometric group theory. Volume 1 : proceedings of the symposium held in Sussex, 1991 / edited by Graham A. Niblo and Martin A. Roller.

Title from PDF title page (viewed on Apr. 9, 2013).

Papers presented at Geometric Group Theory Symposium in Sussex, in 1991.

Includes bibliographical references.

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.

Cover; Title; Copyright; Contents; Preface; List of Participants; Group Actions and Riemann Surfaces; 1. Introduction; 2. The Uniformisation Theorem; 3. Automorphic functions; 4. The geometry of Riemann surfaces; 5. Actions of discrete Mobius groups; 6. Analytic functions again; 7. The epilogue; References; The virtual cohomological dimension of Coxeter groups; Introduction; 1. The construction; 2. Example; References; The Geometric Invariants of a Group: A Survey with Emphasis on the Homotopical Approach; 1. Introduction; 2. Essentially isometric action on R

3. The homotopical geometric invariant4. Criteria and openness result; 5. The homological geometric invariant; 6. Algebraization; 7. Some applications; 8. Polyhedrality; References; String Rewriting -- A Survey for Group Theorists; References; One Relator Products with High-Powered Relators; 1. Introduction; 2. Pictures; 3. Main results; 4. Counterexamples to conjecture F; 5. Applications; References; An Inaccessible Group; 1. Introduction; 2. Constructing the example; 3. Constructing the lattice; References; Isoperimetric and Isodiametric Functions of Finite Presentations

1. Introduction and definitions2. Relation with the word problem; 3. Examples and applications; 4. Relation with peak reduction algorithms; References; On Hilbert's Metric for Simplices; 1. Generalities on Hilbert metrics; 2. The case of simplices; 3. Remarks and questions; References; Software for Automatic Groups, Isomorphism Testing and Finitely Presented Groups; Introduction; 1. Automata; 2. Isomorphism testing; 3. Quotpic; References; Proving Certain Groups Infinite; References; Some Applications of Small Cancellation Theory to One-Relator Groups and One-Relator Products; Introduction

1. The non-small cancellation groups2. The extended small cancellation theory; 3. Solution of the conjugacy problem; 4. One relator products; References; A Group Theoretic Proof of the Torus Theorem; 1. Introduction; 2. Deduction of the Torus Theorem from Theorem 1.2; 3. Poincare duality groups; 4. Ends of pairs of groups; 5. The proof of Theorem 1.2; References; N-Torsion and Applications; 0. Introduction; 1. N-torsion; 2. An example; 3. Topological applications; References; Surface Groups and Quasi-Convexity; Introduction; 1. Quasi-convex subgroups; 2. Surface groups

3. An example in dimension three4. Remarks; 5. Rational structures on groups; References; Constructing Group Actions on Trees; Introduction; 1. Types of group actions on trees; 2. Trees and nested sets; References; Brick's Quasi Simple Filtrations for Groups and 3-Manifolds; 1. Polyhedral niceties; 2. Quasi simple filtration; 3. Qsf-covered polyhedra and groups; 4. Immersions and towers; 5. Unions of qsf spaces; 6. Universal covers of 3-manifolds; 7. Further problems; References; A Note on Accessibility; References; Geometric Group Theory 1991 Problem List

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