Hitchin字符和测地线分层

IF 4.9 1区 数学 Q1 MATHEMATICS
F. Bonahon, G. Dreyer
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引用次数: 22

摘要

对于闭合曲面S, Hitchin分量Hitn(S)是由基群- 1(S)到李群PSLn(R)的群同态组成的特征变体的优选分量。我们构造了一个参数化的希钦分量,它很好地适应了表面上的测地线分层。这是Thurston对Teichmuller空间T(S)的参数化的自然扩展,该参数化是通过与S相关的剪切坐标,对应于n = 2的情况。然而,在这种更高维度的情况下,需要明显的新想法。本文最后给出了几个应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
HITCHIN CHARACTERS AND GEODESIC LAMINATIONS
For a closed surface S, the Hitchin component Hitn(S) is a preferred component of the character variety consisting of group homomorphisms from the fundamental group �1(S) to the Lie group PSLn(R). We construct a parametrization of the Hitchin component that is well-adapted to a geodesic laminationon the surface. This is a natural extension of Thurston's parametrization of the Teichmuller space T(S) by shear coordinates associated to �, corresponding to the case n = 2. However, significantly new ideas are needed in this higher dimensional case. The article concludes with a few applications.
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来源期刊
Acta Mathematica
Acta Mathematica 数学-数学
CiteScore
6.00
自引率
2.70%
发文量
6
审稿时长
>12 weeks
期刊介绍: Publishes original research papers of the highest quality in all fields of mathematics.
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