Title

Exceptional Points for Finitely Generated Fuchsian Groups of the First Kind

Document Type

Book Chapter

Publication Date

2019

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

Book chapter in Advances in Geometry, Grundhofer & Joswig, Eds.

DOI

10.1515/advgeom-2019-0013


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