Bounded Cohomology and Geometry

Abstract

This work deals with relations between a bounded cohomological invariant and the geometry of Hermitian symmetric spaces of noncompact type. The invariant, obtained from the Kähler class, is used to define and characterize a special class of totally geodesic embeddings, called "tight embeddings". In addition, special isometric actions of finitely generated groups on Hermitian symmetric spaces are studied. Results of a joint work with M. Burger and A. Iozzi about surface group representations are also discussed.

Author's Ph.D. thesis, 126 pages

References in corpus (1)

• Surface group representations in PU(p,q) and Higgs bundles

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• A two-cocycle on the group of symplectic diffeomorphisms
• The action of the mapping class group on maximal representations
• Cross Ratios, Anosov Representations and the Energy Functional on Teichmuller Space