Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 39, 2014, 463-472

EXCEPTIONAL POINTS FOR COCOMPACT FUCHSIAN GROUPS

Joseph Fera

Lehman College CUNY, Department of Mathematics and Computer Science
250 Bedford Park Blvd West, Bronx, NY 10468, U.S.A.; joseph.fera 'at' lehman.cuny.edu

Abstract. Let G be a cocompact Fuchsian group acting on the hyperbolic plane H. If G covers a compact hyperbolic surface of genus g \geq 2, then almost every Dirichlet region for G has 12g - 6 sides. In this article, we study the exceptional points for G, i.e., the points in H associated to Dirichlet regions for G with strictly less than 12g - 6 sides. More specifically, we show that uncountably many exceptional points exist for any cocompact group. We also define and prove the existence of higher order exceptional points for any such group.

2010 Mathematics Subject Classification: Primary 20H10; Secondary 30F10.

Key words: Cocompact Fuchsian groups, Dirichlet regions.

Reference to this article: J. Fera: Exceptional points for cocompact Fuchsian groups. Ann. Acad. Sci. Fenn. Math. 39 (2014), 463-472.

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doi:10.5186/aasfm.2014.3917