Tight Homomorphisms and Hermitian Symmetric Spaces |
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Authors: | Marc Burger Alessandra Iozzi Anna Wienhard |
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Affiliation: | 1. FIM, ETH Zentrum, R?mistrasse 101, CH-8092, Zürich, Switzerland 2. Department Mathematik, ETH Zentrum, R?mistrasse 101, CH-8092, Zürich, Switzerland 3. Department of Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ, 08540, USA
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Abstract: | 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. |
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