Geometric Group Theory

doi:10.1017/CBO9780511661860

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.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-vi
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Preface
pp vii-viii
- By Graham A. Niblo, Mathematics Department, Southampton University, Southampton, SO9 5NH, England, Martin A. Roller, Mathematik, Universität Regensburg, Postfach 397, 8400 Regensburg, Germany
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List of Participants
pp ix-x
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1 - Group Actions and Riemann Surfaces
pp 1-18
- By Alan F. Beardon, Department of Mathematics and Mathematical Statistics, University of Cambridge, 16 Mill Lane, Cambridge, CB2 1SB.
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2 - The Virtual Cohomological Dimension of Coxeter Groups
pp 19-23
- By Mladen Bestvina, Mathematics Department, UCLA, Los Angeles, California, CA 90024, USA.
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3 - The Geometric Invariants of a Group A Survey with Emphasis on the Homotopical Approach
pp 24-36
- By Robert Bieri, Fachbereich Mathematik, Universität Frankfurt, Robert-Mayer-Str. 6, D 6000 Frankfurt 1, Germany.
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4 - String Rewriting — A Survey for Group Theorists
pp 37-47
- By Daniel E. Cohen, Department of Mathematics, Queen Mary and Westfield College, Mile End Road, London, E1 4NS.
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5 - One Relator Products and High-Powered Relators
pp 48-74
- By Andrew J. Duncan, Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS., James Howie, Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS.
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6 - An Inaccessible Group
pp 75-78
- By Martin J. Dunwoody, Faculty of Mathematical Studies, University of Southampton, Highfield, Southampton SO9 5NH.
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7 - Isoperimetric and Isodiametric Functions of Finite Presentations
pp 79-96
- By Steve M. Gersten, Mathematics Department, University of Utah, Salt Lake City, UT 84112, USA.
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8 - On Hibert's Metric for Simplices
pp 97-119
- By Pierre de la Harpe, Section de Mathématiques, Université de Genève, 2–4 rue du Lièvre, C.P. 240, 1211 Genève 24, Switzerland.
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9 - Software for Automatic Groups, Isomorphism Testing and Finitely Presented Groups
pp 120-125
- By Derek F. Holt, Mathematics Institute, University of Warwick, Coventry CV4 7AL. Department of Mathematics and Statistics, Merz Court, The University, Newcastle-upon-Tyne NE1 7RU., Sarah Rees, Mathematics Institute, University of Warwick, Coventry CV4 7AL. Department of Mathematics and Statistics, Merz Court, The University, Newcastle-upon-Tyne NE1 7RU.
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10 - Proving Certain Groups Infinite
pp 126-131
- By James Howie, Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS., Richard M. Thomas, Department of Computing Studies, University of Leicester, Leicester, LEI 7RH.
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11 - Some Applications of Small Cancellation Theory to One-Relator Groups and One-Relator Products
pp 132-137
- By Arye Juhász, Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel.
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12 - A Group Theoretic Proof of the Torus Theorem
pp 138-158
- By Peter H. Kropholler, School of Mathematical Sciences, Queen Mary and Westfield College, Mile End Road, London El 4NS.
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13 - N-Torsion and Applications
pp 159-168
- By Martin Lustig, Mathematisches Institut, Ruhr-Universitat Bochum, D 4630 Bochum 1, Germany., Yoav Moriah, Department of Mathematics, Technion, Haifa 32000, Israel.
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14 - Surface Groups and Quasi-Convexity
pp 169-175
- By Christophe Pittet, Section de Mathématiques, Université de Genève, 2–4 rue du Lièvre, C.P. 240, 1211 Geneve 24, Switzerland.
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15 - Constructing Group Actions on Trees
pp 176-187
- By Martin A. Roller, Mathematik, Universität Regensburg, Postfach 397, 8400 Regensburg, Germany.
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16 - Brick's Quasi Simple Filtrations and 3-Manifolds
pp 188-203
- By John R. Stallings, University of California, Berkeley, California, CA 94708, USA.
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17 - A Note on Accessibility
pp 204-207
- By G. A. Swarup, Department of Mathematics, University of Melbourne, Melbourne, Australia.
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18 - Geometric Group Theory 1991 Problem List
pp 208-212
- By Graham A. Niblo, Mathematics Department, Southampton University, Southampton, SO9 5NH.
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Geometric Group Theory

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

List of Participants
pp ix-x

1 - Group Actions and Riemann Surfaces
pp 1-18

2 - The Virtual Cohomological Dimension of Coxeter Groups
pp 19-23

3 - The Geometric Invariants of a Group A Survey with Emphasis on the Homotopical Approach
pp 24-36

4 - String Rewriting — A Survey for Group Theorists
pp 37-47

5 - One Relator Products and High-Powered Relators
pp 48-74

6 - An Inaccessible Group
pp 75-78

7 - Isoperimetric and Isodiametric Functions of Finite Presentations
pp 79-96

8 - On Hibert's Metric for Simplices
pp 97-119

9 - Software for Automatic Groups, Isomorphism Testing and Finitely Presented Groups
pp 120-125

10 - Proving Certain Groups Infinite
pp 126-131

11 - Some Applications of Small Cancellation Theory to One-Relator Groups and One-Relator Products
pp 132-137

12 - A Group Theoretic Proof of the Torus Theorem
pp 138-158

13 - N-Torsion and Applications
pp 159-168

14 - Surface Groups and Quasi-Convexity
pp 169-175

15 - Constructing Group Actions on Trees
pp 176-187

16 - Brick's Quasi Simple Filtrations and 3-Manifolds
pp 188-203

17 - A Note on Accessibility
pp 204-207

18 - Geometric Group Theory 1991 Problem List
pp 208-212

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Geometric Group Theory

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