Finsler bordifications of symmetric and certain locally symmetric spaces
By Michael Kapovich, B. Leeb. Geometry and Topology, 2015
47 citations recorded by the source corpus.
We give a geometric interpretation of the maximal Satake compactification of symmetric spaces $X=G/K$ of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable $G$-invariant Finsler metric on $X$. As an application, we establish the existence of natural bordifications, as orbifolds-with-corners, of locally symmetric spaces $X/\Gamma$ for arbitrary discrete subgroups $\Gamma< G$. These bordifications result from attaching $\Gamma$-quotients of suitable domains of proper discontinuity at infinity. We further prove that such bordifications are compactifications in the case of Anosov subgroups. We show, conversely, that Anosov subgroups are characterized by the existence of such compactifications among uniformly regular subgroups. Along the way, we give a positive answer, in the torsion free case, to a question of Ha\"issinsky and Tukia on convergence groups regarding the cocompactness of their actions on the domains of discontinuity.
Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/1d7fbb5580128ad64ba946713265fffa94f8c5b1
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In Applied Mathematics
In Astronomy and Astrophysics
In Geometry and Topology
- J. Porti
- Michael Kapovich
- B. Leeb
- Anna Wienhard
- Jean-Marc Schlenker
- Bruce Kleiner
- Cornelia Drutu
- M. Boileau
Citations in the corpus
- Anosov subgroups: dynamical and geometric characterizations (2017, methodology): “(v) In our paper [15] we establish two more characterizations of Anosov subgroups among uniformly regular subgroups, namely as coarse retracts and by S-cocompactness.”
- Dynamics on flag manifolds: domains of proper discontinuity and cocompactness (2013, methodology): “We give a geometric treatment and present the material in a form suitable for the further development of our theory of discrete isometry groups acting on Riemannian symmetric spaces and euclidean buildings, such as in our papers [16; 20].”