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On the properness of some algebraic equations appearing in Fuchsian Groups

Díaz Sánchez, Raquel and Ushijima, Akira (2009) On the properness of some algebraic equations appearing in Fuchsian Groups. Topology Proceedings, 33 . pp. 81-106. ISSN 0146-4124

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Abstract

In this paper we give necessary and sufficient conditions on three orientation-preserving hyperbolic isometries T1,T2,T3 so that for any point x ∈ H2 the orthogonal bisectors of the three segments with endpoints x, Ti(x) intersect. This is equivalent to proving the properness of certain algebraic sets. As a corollary, we give a new proof for the existence and density of generic fundamental polygons for cocompact Fuchsian groups.

Item Type:Article
Uncontrolled Keywords:Fuchsian groups and automorphic functions; Moduli of Riemann surfaces, Teichmüller theory
Subjects:Sciences > Mathematics > Geometry
ID Code:15715
References:

A. F. Beardon. The geometry of discrete groups, volume 91 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. Corrected reprint of the 1983 original.

M. Berger Geometry II, Springer: Berlin, 1996.

T. Jorgensen and A. Marden. Generic Fundamental Polyhedra for Kleinian Groups, holomorphic Functions and Moduli, Vol. II (Berkeley, CA, 1986), Math. Sci. Res. Inst. Publ., vol. 11 , Springer, New York, 1988, pp. 69-85.

J. M. Montesinos, Classical Tessellations and Three-Manifolds, Springer-Verlag, 1985.

L. Santaló Geometrías no euclidianas, Ed. Universitaria de Buenos Aires: Eudeba, 1961.

Deposited On:21 Jun 2012 10:35
Last Modified:21 Jun 2012 10:35

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