Exceptional Points for Finitely Generated Fuchsian Groups of the First Kind

Document Type

Peer-Reviewed Article

Publication Date

2020

Abstract

Let G be a finitely generated Fuchsian group of the first kind and let (g : m1, m2, …, mn) be its shortened signature. Beardon showed that almost every Dirichlet region for G has 12g + 4n − 6 sides. Points in ℍ corresponding to Dirichlet regions for G with fewer sides are called exceptional for G. We generalize previously established methods to show that, for any such G, its set of exceptional points is uncountable.

Comments

Advances in Geometry, Grundhofer & Joswig, Eds. ISSN 1615-715X

DOI

10.1515/advgeom-2019-0013

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