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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.

Discrete groups --- Geometry --- Groups, Discrete --- Discrete mathematics --- Infinite groups

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Topological groups. Lie groups --- Number theory --- Automorphic functions --- Discrete groups --- Congresses --- 511 --- -Discrete groups --- -Groups, Discrete --- Infinite groups --- Fuchsian functions --- Functions, Automorphic --- Functions, Fuchsian --- Functions of several complex variables --- -Number theory --- 511 Number theory --- -511 Number theory --- Groups, Discrete --- Congresses. --- Finite groups --- Groupes finis --- Discrete mathematics --- Discrete groups - Congresses --- Automorphic functions - Congresses