Higher Teichmüller Spaces: from SL(2,R) to other Lie groups

Details Higher Teichmüller Spaces: from SL(2,R) to other Lie groups Higher Teichmüller Spaces: from SL(2,R) to other Lie groups

2010-04-16

arxiv.org/abs/1004.2894v4

Mathematics

Geometric Topology

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Scientific paper

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.

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