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

By M. Burger, A. Iozzi, Anna Wienhard. 2010

67 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2819a9a8f193ffaa6bf783c5dc8a0dc1432d56ae

Citations in the corpus

• Convex cocompactness in pseudo-Riemannian hyperbolic spaces (2017, unknown): “[14]); they sharemany dynamical properties with classical convex cocompact subgroups of rank-one simple Lie groups (see in particular [30,34,35,38]).”