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

## 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 |
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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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