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BY 4.0 license Open Access Published by De Gruyter Open Access December 31, 2019

On Infinitely generated Fuchsian groups of the Loch Ness monster, the Cantor tree and the Blooming Cantor tree

  • John A. Arredondo EMAIL logo and Camilo Ramírez Maluendas
From the journal Complex Manifolds


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.

MSC 2010: 20H10; 57N05; 57N16


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Received: 2019-08-28
Accepted: 2019-10-31
Published Online: 2019-12-31

© 2020 John A. Arredondo et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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