Generic fundamental polygons for Fuchsian groups

Akira Ushijima

Vol. 251 (2011), No. 2, 453–468

DOI: 10.2140/pjm.2011.251.453

Abstract

A Dirichlet fundamental polygon for a Fuchsian group is said to be generic if its combinatorial shape is stable under any small permutation of the center of the polygon. Almost all points in the hyperbolic plane are known to be centers of generic fundamental polygons. We prove that the same property holds for points in the boundary of the hyperbolic plane.

Keywords

Fuchsian group, fundamental polygon

Mathematical Subject Classification 2000

Primary: 20H10

Secondary: 57M60

Milestones

Received: 6 May 2010

Revised: 16 February 2011

Accepted: 7 March 2011

Published: 3 June 2011