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Finsler bordifications of
symmetric and certain locally symmetric spaces
Michael Kapovich and Bernhard Leeb |
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Geometry & Topology 22 (2018) 2533–2646
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Abstract |
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We give a geometric interpretation of the maximal Satake compactification of symmetric spaces of noncompact type, showing that it arises by attaching the horofunction boundary for a suitable –invariant Finsler metric on . As an application, we establish the existence of natural bordifications, as orbifolds-with-corners, of locally symmetric spaces for arbitrary discrete subgroups . These bordifications result from attaching –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 Haïssinsky and Tukia on convergence groups regarding the cocompactness of their actions on the domains of discontinuity. |
Keywords
discrete groups, Finsler geometry
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Mathematical Subject Classification 2010
Primary: 20F65, 22E40, 53C35
Secondary: 51E24, 53B40
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References |
Publication
Received: 14 March 2016
Revised: 6 July 2017
Accepted: 3 February 2018
Published: 1 June 2018
Proposed: Bruce Kleiner
Seconded: Jean-Pierre Otal, Tobias H Colding
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Authors |
| Michael Kapovich | |
| MK: Department of Mathematics University of California, Davis Davis, CA United States |
MK: Korea Institute for Advanced
Study Seoul South Korea |
| Bernhard Leeb | |
| BL: Mathematisches Institut Universität München München Germany |
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