Exceptional points for finitely generated Fuchsian groups of the first kind
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Joseph Fera
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.
Communicated by: J. Ratcliffe
Acknowledgement
The authors wish to thank the referee of this manuscript for providing detailed comments which improved the paper’s readability and resolved some technical issues.
References
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Articles in the same Issue
- Frontmatter
- Topology of tropical moduli of weighted stable curves
- Classification of slant surfaces in 𝕊3 × ℝ
- New dense superball packings in three dimensions
- Explicit computation of some families of Hurwitz numbers, II
- An extension theorem for non-compact split embedded Riemannian symmetric spaces and an application to their universal property
- Moduli of stable sheaves supported on curves of genus three contained in a quadric surface
- Exceptional points for finitely generated Fuchsian groups of the first kind
- Tropical superelliptic curves
- Differentiability of projective transformations in dimension 2
- On pseudo-Einstein real hypersurfaces
- On the moduli spaces of singular principal bundles on stable curves
- Three-dimensional connected groups of automorphisms of toroidal circle planes
