On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree
In this paper, for a non-compact Riemman surface S homeomorphic to either: the Infinite Loch Ness monster, the Cantor tree and the Blooming Cantor tree, we give a precise description of an infinite set of generators of a Fuchsian group Γ < PSL(2, ℝ), such that the quotient space ℍ/Γ is a hyperbol...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | article |
| Language: | EN |
| Published: |
De Gruyter
2019
|
| Subjects: | |
| Online Access: | https://doaj.org/article/ac5943e8a7ca4fae91f8689d54de80eb |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this paper, for a non-compact Riemman surface S homeomorphic to either: the Infinite Loch Ness monster, the Cantor tree and the Blooming Cantor tree, we give a precise description of an infinite set of generators of a Fuchsian group Γ < PSL(2, ℝ), such that the quotient space ℍ/Γ is a hyperbolic Riemann surface homeomorphic to S. For each one of these constructions, we exhibit a hyperbolic polygon with an infinite number of sides and give a collection of Mobius transformations identifying the sides in pairs. |
|---|