Topology Proceedings 33 (2009), pp. 81-106

On the properness of some algebraic equations appearing in Fuchsian groups

Raquel Díaz and Akira Ushijima

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, T_i(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.

Keywords: Fuchsian groups, fundamental polygons

Mathematics Subject Classification: 20H10 22E40 (32G15)

Document formats: PDF file 251.4 Kb

Topology Proceedings, Volume 33 (2009)
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