Geometric and Functional Analysis

, Volume 19, Issue 3, pp 678–721 | Cite as

Tight Homomorphisms and Hermitian Symmetric Spaces

  • Marc Burger
  • Alessandra IozziEmail author
  • Anna Wienhard


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 Poincaré disk.

Keywords and phrases

Hermitian symmetric spaces bounded cohomology Shilov boundary totally geodesic embedding tight homomorphism 

2000 Mathematics Subject Classification

53C24 53C35 32M15 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.FIM, ETH ZentrumZürichSwitzerland
  2. 2.Department MathematikETH ZentrumZürichSwitzerland
  3. 3.Department of MathematicsPrinceton UniversityPrincetonUSA

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