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Mathematics > Differential Geometry

arXiv:0710.5641 (math)
[Submitted on 30 Oct 2007 (v1), last revised 15 Sep 2008 (this version, v2)]

Title:Tight homomorphisms and Hermitian symmetric spaces

Authors:Marc Burger, Alessandra Iozzi, Anna Wienhard
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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 Poincare' disk.
Comments: 51 pages, no figure. The exposition has been improved, especially in the Introduction
Subjects: Differential Geometry (math.DG)
Cite as: arXiv:0710.5641 [math.DG]
  (or arXiv:0710.5641v2 [math.DG] for this version)
  https://doi.org/10.48550/arXiv.0710.5641

Submission history

From: Alessandra Iozzi [view email]
[v1] Tue, 30 Oct 2007 13:27:56 UTC (51 KB)
[v2] Mon, 15 Sep 2008 12:00:33 UTC (63 KB)
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