J Austral Math Soc Ser A 47 pp350--367, 1989.

Geometry of Neumann Subgroups

Ravi S. Kulkarni

Abstract

A Neumann subgroup of the classical modular group is by definition a complement of a maximal parabolic subgroup. Recently Neumann subgroups have been studied in a series of papers by Brenner and Lyndon. There is a natural extension of the notion of a Neumann subgroup in the context of any finitely generated Fuchsian group G acting on the hyperbolic plane H such that G\H is homeomorphic to an open disk. Using a new geometric method we extend the work of Brenner and Lyndon in this more general context.

1980 AMS Subject Classification (1985 Revision): 20E28

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Authors

Ravi S. Kulkarni

Department of Mathematics, City University of New York, 33 W. 42nd Street, New York, New York 10036-8099, U.S.A.