Bounded Cohomology and Geometry

2005/01/17 by Anna Wienhard
Mathematics · #math.DG #math.GR #msc:53C35 #msc:22E40 #msc:32M15

paper · pdf

published as Bonner Mathematische Schriften Nr. 368, Bonn 2004 · Author's Ph.D. thesis, 126 pages

arxiv created 2005/01/17 · arxiv updated 2009/12/01

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.

Related

• Tight homomorphisms and Hermitian symmetric spaces
• Equivariant embeddings of Hermitian symmetric spaces
• A characterization of higher rank symmetric spaces via bounded cohomology
• Classification of tight homomorphisms
• Hermitian symmetric space, flat bundle and holomorphicity criterion