Computational and Geometric Aspects of Modern Algebra

doi:10.1017/CBO9780511600609

This book comprises a collection of papers from participants at the IMCS Workshop on Computational and Geometric Aspects of Modern Algebra, held at Heriot-Watt University in 1998. Written by leading researchers, the papers cover a wide range of topics in the vibrant areas of word problems in algebra and geometric group theory. This book represents a timely record of recent work and provides an indication of the key areas of future development.

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Contents

Frontmatter
pp i-iv
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Contents
pp v-v
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Foreword
pp vi-vi
- By M D Atkinson, N D Gilbert, J Howie, S A Linton, E F Robertson
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Participants
pp vii-viii
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1 - Lie Methods in Growth of Groups and Groups of Finite Width
pp 1-27
- By Laurent Bartholdi, Rostislav I. Grigorchuk
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2 - Translation numbers of groups acting on quasiconvex spaces
pp 28-38
- By Gregory R. Conner
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3 - On a term rewriting system controlled by sequences of integers
pp 39-53
- By Aleš Drápal
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4 - On certain finite generalized tetrahedron groups
pp 54-65
- By Martin Edjvet, Gerhard Rosenberger, Michael Stille, Richard M. Thomas
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5 - Efficient computation in word-hyperbolic groups
pp 66-77
- By David B. A. Epstein, Derek F. Holt
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6 - Constructing hyperbolic manifolds
pp 78-86
- By B. Everitt, C. MacLachlan
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7 - Computing in groups with exponent six
pp 87-100
- By George Havas, M. F. Newman, Alice C. Niemeyer, Charles C. Sims
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8 - Rewriting as a special case of non-commutative Gröbner basis theory
pp 101-105
- By Anne Heyworth
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9 - Detecting 3-manifold presentations
pp 106-119
- By Cynthia Hog-Angeloni
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10 - In search of a word with special combinatorial properties
pp 120-127
- By Štěpán Holub
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11 - Cancellation diagrams with non-positive curvature
pp 128-149
- By Günther Huck, Stephan Rosebrock
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12 - Some Applications of Prefix-Rewriting in Monoids, Groups, and Rings
pp 150-191
- By Klaus Madlener, Friedrich Otto
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13 - Verallgemeinerte Biasinvarianten und ihre Berechnung
pp 192-207
- By Wolfgang Metzler
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14 - On groups which act freely and properly on finite dimensional homotopy spheres
pp 208-228
- By Guido Mislin, Olympia Talelli
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15 - On Confinal Dynamics of Rooted Tree Automorphisms
pp 229-245
- By V V Nekrashevych, V I Sushchansky
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16 - An asymptotic invariant of surface groups
pp 246-253
- By Amnon Rosenmann
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17 - A cutpoint tree for a continuum
pp 254-265
- By Eric L Swenson
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18 - Generalised triangle groups of type (2, m, 2)
pp 266-279
- By Alun G T Williams
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Computational and Geometric Aspects of Modern Algebra

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Contents

Frontmatter
pp i-iv

Contents
pp v-v

Foreword
pp vi-vi

Participants
pp vii-viii

1 - Lie Methods in Growth of Groups and Groups of Finite Width
pp 1-27

2 - Translation numbers of groups acting on quasiconvex spaces
pp 28-38

3 - On a term rewriting system controlled by sequences of integers
pp 39-53

4 - On certain finite generalized tetrahedron groups
pp 54-65

5 - Efficient computation in word-hyperbolic groups
pp 66-77

6 - Constructing hyperbolic manifolds
pp 78-86

7 - Computing in groups with exponent six
pp 87-100

8 - Rewriting as a special case of non-commutative Gröbner basis theory
pp 101-105

9 - Detecting 3-manifold presentations
pp 106-119

10 - In search of a word with special combinatorial properties
pp 120-127

11 - Cancellation diagrams with non-positive curvature
pp 128-149

12 - Some Applications of Prefix-Rewriting in Monoids, Groups, and Rings
pp 150-191

13 - Verallgemeinerte Biasinvarianten und ihre Berechnung
pp 192-207

14 - On groups which act freely and properly on finite dimensional homotopy spheres
pp 208-228

15 - On Confinal Dynamics of Rooted Tree Automorphisms
pp 229-245

16 - An asymptotic invariant of surface groups
pp 246-253

17 - A cutpoint tree for a continuum
pp 254-265

18 - Generalised triangle groups of type (2, m, 2)
pp 266-279

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Computational and Geometric Aspects of Modern Algebra

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