Tameness of Riemannian locally symmetric spaces arising from Anosov representations

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.