Discrete isometry groups of symmetric spaces
- Author(s): Kapovich, Michael;
- Leeb, Bernhard
- et al.
Published Web Locationhttps://arxiv.org/pdf/1703.02160.pdf
This survey is based on a series of lectures that we gave at MSRI in Spring 2015 and on a series of papers, mostly written jointly with Joan Porti. Our goal here is to: 1. Describe a class of discrete subgroups Γ lt; G of higher rank semisimple Lie groups, which exhibit some "rank 1 behavior". 2. Give different characterizations of the subclass of Anosov subgroups, which generalize convex-cocompact subgroups of rank 1 Lie groups, in terms of various equivalent dynamical and geometric properties (such as asymptotically embedded, RCA, Morse, URU). 3. Discuss the topological dynamics of discrete subgroups Γ on flag manifolds associated to G and Finsler compactifications of associated symmetric spaces X=G/K. Find domains of proper discontinuity and use them to construct natural bordifications and compactifications of the locally symmetric spaces X/Γ.