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

Abstract

The first part of this paper surveys several characterizations of Teichmüller 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 Teichmüller 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.

The file uploaded on May 12th was the wrong one and did not contain the Section 4.6 that was added. This is the version to appear in the Handbook of Teichmüller theory

References in corpus (3)

• Topological Invariants of Anosov Representations
• Quasi-morphisms on Free Groups
• Density of Zariski density for surface groups

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• Studying Deformations of Fuchsian Representations with Higgs Bundles
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• Volume invariant and maximal representations of discrete subgroups of Lie groups
• Tangent spaces to the Teichmueller space from the energy-conscious perspective
• A note on Reidemeister Torsion of G-Anosov Representations
• On Moduli Spaces of Convex Projective Structures on Surfaces: Outitude and Cell-Decomposition in Fock-Goncharov Coordinates
• The Gromov norm of the quaternionic Kähler class
• A Family of Quasimorphism Constructions