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Morse actions of discrete
groups on symmetric spaces: local-to-global principle
Michael Kapovich, Bernhard Leeb and Joan Porti |
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Geometry & Topology 29 (2025) 2343–2390
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Abstract |
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Our main result is a local-to-global principle for Morse quasigeodesics, maps and actions. As an application of our techniques we show algorithmic recognizability of Morse actions and construct Morse “Schottky subgroups” of higher-rank semisimple Lie groups via arguments not based on Tits ping-pong. Our argument is purely geometric and proceeds by constructing equivariant Morse quasiisometric embeddings of trees into higher-rank symmetric spaces. |
Keywords
symmetric spaces, quasigeodesics, discrete subgroups
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Mathematical Subject Classification
Primary: 22E40, 53C35
Secondary: 20F65
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References |
Publication
Received: 9 January 2023
Revised: 26 May 2024
Accepted: 4 January 2025
Published: 14 August 2025
Proposed: Bruce Kleiner
Seconded: Tobias H Colding, David Fisher
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Authors |
| Michael Kapovich | |
| Department of Mathematics University of California, Davis Davis, CA United States |
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| Bernhard Leeb | |
| Mathematisches Institut Universität München München Germany |
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| Joan Porti | |
| Departament de Matemàtiques and
Centre de Recerca Matemàtica Universitat Autònoma de Barcelona Barcelona Spain |
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| © 2025 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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