Higher Teichmüller Spaces: from SL(2,R) to other Lie groups
Higher Teichmüller Spaces: from SL(2,R) to other Lie groups
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更高的 Teichmüller 空间：从 SL(2,R) 到其他李群
DOI：
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发表时间：
2010
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通讯作者：
Anna Wienhard
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文献类型：
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作者：
M. Burger;A. Iozzi;Anna Wienhard
本文第一部分讨论了作为曲面基本群表示空间的子集的Teichm-Uller空间到PSL(2，R)的几个特征，特别强调了当PSL(2，R)被Hermitian型李群取代时推广的(有界)上同调不变量.第二部分讨论了两类高阶Teichm-Uller空间的基本结构，即Hermitian型李群的极大表示空间和分裂实单李群的Hitchin表示或正表示空间.
The first part of this paper surveys several characterizations of Teichm"uller space as a subset of the space of representation of the fundamental group of a surface into PSL(2,R). Special emphasis is put on (bounded) cohomological invariants which generalize when PSL(2,R) is replaced by a Lie group of Hermitian type. The second part discusses underlying structures of the two families of higher Teichm"uller spaces, namely the space of maximal representations for Lie groups of Hermitian type and the space of Hitchin representations or positive representations for split real simple Lie groups.