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...
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De Gruyter
2019
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oai:doaj.org-article:ac5943e8a7ca4fae91f8689d54de80eb2021-12-02T17:14:47ZOn Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree2300-744310.1515/coma-2020-0004https://doaj.org/article/ac5943e8a7ca4fae91f8689d54de80eb2019-12-01T00:00:00Zhttps://doi.org/10.1515/coma-2020-0004https://doaj.org/toc/2300-7443In 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.Arredondo John A.Maluendas Camilo RamírezDe Gruyterarticleinfinite loch ness monstercantor treeblooming cantor treegeometric schottky groupsnoncompact surfaces20h1057n0557n16MathematicsQA1-939ENComplex Manifolds, Vol 7, Iss 1, Pp 73-92 (2019) |
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EN |
| topic |
infinite loch ness monster cantor tree blooming cantor tree geometric schottky groups noncompact surfaces 20h10 57n05 57n16 Mathematics QA1-939 |
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infinite loch ness monster cantor tree blooming cantor tree geometric schottky groups noncompact surfaces 20h10 57n05 57n16 Mathematics QA1-939 Arredondo John A. Maluendas Camilo Ramírez On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree |
| description |
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. |
| format |
article |
| author |
Arredondo John A. Maluendas Camilo Ramírez |
| author_facet |
Arredondo John A. Maluendas Camilo Ramírez |
| author_sort |
Arredondo John A. |
| title |
On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree |
| title_short |
On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree |
| title_full |
On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree |
| title_fullStr |
On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree |
| title_full_unstemmed |
On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree |
| title_sort |
on infinitely generated fuchsian groups of the loch ness monster, the cantor tree and the blooming cantor tree |
| publisher |
De Gruyter |
| publishDate |
2019 |
| url |
https://doaj.org/article/ac5943e8a7ca4fae91f8689d54de80eb |
| work_keys_str_mv |
AT arredondojohna oninfinitelygeneratedfuchsiangroupsofthelochnessmonsterthecantortreeandthebloomingcantortree AT maluendascamiloramirez oninfinitelygeneratedfuchsiangroupsofthelochnessmonsterthecantortreeandthebloomingcantortree |
| _version_ |
1718381278827380736 |