On Infinite Discontinuous Groups

Max Dehn

A chapter in Papers on Group Theory and Topology, 1987, pp 133-178 from Springer

Abstract: Abstract The general discontinuous group is given by n generators and m relations between them $$ \begin{array}{*{20}c} {\text{R}_\text{1} \text{(S}_{\text{i}_\text{1} } \ldots ) = 1} \\ { \ldots \ldots \ldots \ldots \ldots } \\ {\text{R}_\text{m} \text{(S}_{\text{i}_\text{m} } \ldots ) = 1,} \\ \end{array} $$ as first defined by Dyck (Math. Ann., 20 and 22). The results of those works, however, relate essentially to finite groups. The general theory of groups defined in this way at present appears very undeveloped in the infinite case. Here there are above all three fundamental problems whose solution is very difficult and which will not be possible without a penetrating study of the subject.

Keywords: Fundamental Group; Surface Curve; Closed Surface; Hyperbolic Plane; Transformation Problem (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-1-4612-4668-8_8

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