Tight homomorphisms and Hermitian symmetric spaces

Details Tight homomorphisms and Hermitian symmetric spaces Tight homomorphisms and Hermitian symmetric spaces

2007-10-30

arxiv.org/abs/0710.5641v2

Mathematics

Differential Geometry

51 pages, no figure. The exposition has been improved, especially in the Introduction

Scientific paper

We introduce the notion of tight homomorphism into a locally compact group with nonvanishing bounded cohomology and study these homomorphisms in detail when the target is a Lie group of Hermitian type. Tight homomorphisms between Lie groups of Hermitian type give rise to tight totally geodesic maps of Hermitian symmetric spaces. We show that tight maps behave in a functorial way with respect to the Shilov boundary and use this to prove a general structure theorem for tight homomorphisms. Furthermore we classify all tight embeddings of the Poincare' disk.

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