关于尼斯湖水怪，康托树和盛开的康托树的无限生成的Fuchsian群

IF 0.5 Q3 MATHEMATICS

Complex Manifolds Pub Date : 2019-12-31 DOI:10.1515/coma-2020-0004

John A. Arredondo, Camilo Ramírez Maluendas

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引用次数: 3

摘要

摘要:对于非紧Riemman曲面S同胚于:对于无限尼斯湖妖、康托树和布卢姆康托树，我们给出了Fuchsian群Γ < PSL(2，∈)的无限生成集的精确描述，使得商空间 /Γ是s同纯的双曲黎曼曲面。对于这些构造中的每一个，我们都给出了一个具有无限条边的双曲多边形，并给出了一组莫比乌斯变换来标识这些边对。

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

Abstract 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.

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来源期刊

Complex Manifolds MATHEMATICS-

CiteScore

1.30

自引率

20.00%

发文量

审稿时长

25 weeks

期刊介绍： Complex Manifolds is devoted to the publication of results on these and related topics: Hermitian geometry, Kähler and hyperkähler geometry Calabi-Yau metrics, PDE''s on complex manifolds Generalized complex geometry Deformations of complex structures Twistor theory Geometric flows on complex manifolds Almost complex geometry Quaternionic geometry Geometric theory of analytic functions Holomorphic dynamics Several complex variables Dolbeault cohomology CR geometry.