Tameness of Riemannian locally symmetric spaces arising from Anosov representations

2015/08/19 by Olivier Guichard, Guichard, Olivier, Fanny Kassel +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #Mathematics #Pure mathematics #Topological and Geometric Data Analysis #math.GT

paper · pdf · doi:10.48550/arxiv.1508.04759

26 pages; corrected proof of compactness (section 4.3) using dynamical instead of cohomological argument

openalex publication_date 2015/08/19 · arxiv created 2015/09/09 · arxiv updated 2015/09/10 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We construct compactifications of Riemannian locally symmetric spaces arising as quotients by Anosov representations. These compactifications are modeled on generalized Satake compactifications and, in certain cases, on maximal Satake compactifications. We deduce that these Riemannian locally symmetric spaces are topologically tame, i.e. homeomorphic to the interior of a compact manifold with boundary. We also construct domains of discontinuity (not necessarily with a compact quotient) in a much more general setting.

Citations

• Compactification of certain Clifford-Klein forms of reductive homogeneous spaces

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