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On the properness of some algebraic equations appearing in Fuchsian Groups

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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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Official URL: http://topology.auburn.edu/tp/reprints/v33/tp33006p1.pdf


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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
Deposited On:21 Jun 2012 10:35
Last Modified:18 Feb 2019 12:28

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