PSL2R $ {\ mathm {PSL}_2\mathbb{R}} $中纯双曲表示的几何化

IF 0.5 4区数学 Q3 MATHEMATICS

Advances in Geometry Pub Date : 2021-01-01 DOI:10.1515/advgeom-2020-0025

Gianluca Faraco

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引用次数: 0

摘要

设S是g属至少为2的曲面。如果一个表示ρ:π1S→PSL2R $ \rho:\pi_1 S\to{\mathrm{PSL}_2\mathbb{R}} $仅由双曲元和单位元组成，则称其为纯双曲的。我们可能想知道，在什么条件下，s上的分支双曲结构的完整性会出现这样的表征。在这项工作中，我们完全描述了它们，给出了必要和充分条件。

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Geometrisation of purely hyperbolic representations in PSL2R $ {\mathrm{PSL}_2\mathbb{R}} $

Abstract Let S be a surface of genus g at least 2. A representation ρ:π1S→PSL2R $ \rho:\pi_1 S\to{\mathrm{PSL}_2\mathbb{R}} $ is said to be purely hyperbolic if its image consists only of hyperbolic elements along with the identity. We may wonder under which conditions such representations arise as the holonomy of a branched hyperbolic structure on S. In this work we characterise them completely, giving necessary and sufficient conditions.

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来源期刊

Advances in Geometry 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Advances in Geometry is a mathematical journal for the publication of original research articles of excellent quality in the area of geometry. Geometry is a field of long standing-tradition and eminent importance. The study of space and spatial patterns is a major mathematical activity; geometric ideas and geometric language permeate all of mathematics.