2005/12/02 by François Labourie, F. Labourie, Labourie, F.
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Class (philosophy) #Computer science #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Mapping class group #Mathematical analysis #Mathematics #Moduli space #Physics #Pure mathematics #Quantum mechanics #Riemann surface #Space (punctuation) #Surface (topology) #Symplectic geometry #Teichmüller space #math.DG
paper · pdf · doi:10.48550/arxiv.math/0512070
30 pages 30 pages. in this new version, the standard definition of the Toledo invariant is chosen. Theorem 1.0.5 is slightly strenghtened. Various typos are corrected
openalex publication_date 2005/12/02 · arxiv created 2006/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study Hitchin representations and maximal symplectic representations of surface groups, which can be both thought of as generalisations of Fuchsian representations. We show that the corresponding energy functionals are proper on Teichmuller space. We also prove that the mapping class group acts properly on the corresponding moduli spaces. These two results follows from the fact these representations are well displacing which is a consequence they are associated to cross ratios. We state some applications.