Discrete Groups and Geometry

doi:10.1017/CBO9780511565793

This book constitutes the proceedings of a conference held at the University of Birmingham to mark the retirement of Professor A. M. Macbeath. The papers represent up-to-date work on a broad spectrum of topics in the theory of discrete group actions, ranging from presentations of finite groups through the detailed study of Fuchsian and crystallographic groups, to applications of group actions in low dimensional topology, complex analysis, algebraic geometry and number theory. For those wishing to pursue research in these areas, this volume offers a valuable summary of contemporary thought and a source of fresh geometric insights.

‘ … an exemplary overview of the present state of discrete group theory.’

Source: International Mathematical News

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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
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Symmetries of modular surfaces
pp 1-9
- By M. Akbas, D. Singerman, To Murray Macbeath on the occasion of his retirement
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Lifting group actions to covering spaces
pp 10-15
- By M. A. Armstrong, To Murray Macbeath on the occasion of his retirement
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A combinatorial approach to the symmetries of M and M–l Riemann surfaces
pp 16-25
- By E. Bujalance, A. F. Costa, To A. M. Macbeath on the occasion of his retirement
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Inequalities for Pell equations and Fuchsian groups
pp 26-35
- By J. H. H. Chalk, Dedicated to Murray Macbeath on the occasion of his retirement
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The Euler characteristic of graph products and of Coxeter groups
pp 36-46
- By I. M. Chiswell, To Murray Macbeath on the occasion of his retirement
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Infinite families of automorphism groups of Riemann surfaces
pp 47-56
- By Marston D. E. Conder, Ravi S. Kulkarni, Dedicated to A. M. Macbeath with much respect
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Planar hyperelliptic Klein surfaces and fundamental regions of NEC groups
pp 57-65
- By A. F. Costa, E. Martínez
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An example of an infinite group
pp 66-74
- By M. Edjvet, Dedicated to A. M. Macbeath on the occasion of his retirement
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Moduli of Riemann surfaces with symmetry
pp 75-93
- By G. González-Díez, W. J. Harvey, To Murray Macbeath on the occasion of his retirement
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Modular groups – geometry and physics
pp 94-103
- By W. J. Harvey, To Murray Macbeath on the occasion of his retirement
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On automorphisms of free products
pp 104-119
- By A. H. M. Hoare, M. K. F. Lai, for Murray Macbeath
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The growth series of the Gieseking group
pp 120-124
- By D. L. Johnson, H.-J. Song, To Murray Macbeath on the occasion of his retirement
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Exceptional representations of PSL2(q) of monodromy genus zero
pp 125-136
- By G. A. Jones, Dedicated to Murray Macbeath on the occasion of his retirement
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On the rank of NEC groups
pp 137-147
- By R. Kaufmann, H. Zieschang, To Murray Macbeath on the occasion of his retirement
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The geometry of bending quasi-Fuchsian groups
pp 148-164
- By C. Kourouniotis
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Farey series and sums of continued fractions
pp 165-170
- By J. Lehner, To Murray Macbeath, friend and colleague, on his retirement
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Commensurability classes of two-generator Fuchsian groups
pp 171-189
- By C. MacLachlan, G. Rosenberger, To Murray Macbeath on the occasion of his retirement
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Limit points via Schottky pairings
pp 190-195
- By P. J. Nlcholls, P. L. Waterman, Dedicated to A.M. Macbeath
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Diagonalizing Eisenstein series III
pp 196-208
- By R. A. Rankin, To Murray Macbeath on the occasion of his retirement
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Some remarks on 2-generator hyperbolic 3-manifolds
pp 209-219
- By A. W. Reid, To Murray Macbeath on the occasion of his retirement
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Uniformization, graded Riemann surfaces and supersymmetry
pp 220-233
- By P. Teofilatto, Dedicated to A. M. Macbeath on his retirement
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Generating sets for finite groups
pp 234-242
- By R. M. Thomas, To Murray Macbeath on the occasion of his retirement
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Group actions on trees with and without fixed points
pp 243-248
- By D. L. Wllkens, To Murray Macbeath on the occasion of his retirement
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Discrete Groups and Geometry

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Symmetries of modular surfaces
pp 1-9

Lifting group actions to covering spaces
pp 10-15

A combinatorial approach to the symmetries of M and M–l Riemann surfaces
pp 16-25

Inequalities for Pell equations and Fuchsian groups
pp 26-35

The Euler characteristic of graph products and of Coxeter groups
pp 36-46

Infinite families of automorphism groups of Riemann surfaces
pp 47-56

Planar hyperelliptic Klein surfaces and fundamental regions of NEC groups
pp 57-65

An example of an infinite group
pp 66-74

Moduli of Riemann surfaces with symmetry
pp 75-93

Modular groups – geometry and physics
pp 94-103

On automorphisms of free products
pp 104-119

The growth series of the Gieseking group
pp 120-124

Exceptional representations of PSL2(q) of monodromy genus zero
pp 125-136

On the rank of NEC groups
pp 137-147

The geometry of bending quasi-Fuchsian groups
pp 148-164

Farey series and sums of continued fractions
pp 165-170

Commensurability classes of two-generator Fuchsian groups
pp 171-189

Limit points via Schottky pairings
pp 190-195

Diagonalizing Eisenstein series III
pp 196-208

Some remarks on 2-generator hyperbolic 3-manifolds
pp 209-219

Uniformization, graded Riemann surfaces and supersymmetry
pp 220-233

Generating sets for finite groups
pp 234-242

Group actions on trees with and without fixed points
pp 243-248

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Discrete Groups and Geometry

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