Discrete Groups and Geometry

Proceedings of the conference held at the University of Birmingham in honour of Professor A. M. Macbeath. Many interesting papers are included from respected figures, on discrete group theory.

W. J. Harvey (Edited by), C. Maclachlan (Edited by)

9780521429320, Cambridge University Press

Paperback, published 30 July 1992

260 pages
22.9 x 15.1 x 1.8 cm, 0.374 kg

' … an exemplary overview of the present state of discrete group theory.' International Mathematical News

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.

1. Symmetries of modular surfaces
2. On lifting group actions to covering spaces
3. A combinatorial approach to symmetries of M and M-1 Riemann surfaces
4. Euler characteristics of graph products of Coxeter groups
5. Inequalities for Pell equations and Fuchsian groups
6. On regular oriented triangular maps with automorphism group PSL(2,q)
7. An example of an infinite group
8. Moduli spaces of Riemann surfaces with symmetry
9. Modular groups: geometry and physics
10. The Poincaré series of Gieseking groups
11. The mondromy genus of exceptional representations of PSL(2,q)
12. The geometry of bending quasi-Fuchsian groups
13. On the rank of NEC groups
14. Theory of Fuchsian groups
15. Farey series and sums of continued fractions
16. Comensurability classes of 2-generator Fuchsian groups
17. Existence of Garnett points
18. Diagonalising Eisenstein series III
19. Some remarks on 2-generator hyperbolic manifolds
20. Generating sets for finite groups
21. Group actions on R-trees with/without fixed points.

Subject Areas: Topology [PBP], Geometry [PBM], Groups & group theory [PBG]