Morse actions of discrete groups on symmetric spaces: local-to-global principle

Kapovich, Michael¹ ; Leeb, Bernhard² ; Porti, Joan³

¹Department of Mathematics, University of California, Davis, Davis, CA, United States
²Mathematisches Institut, Universität München, München, Germany
³Departament de Matemàtiques and Centre de Recerca Matemàtica, Universitat Autònoma de Barcelona, Barcelona, Spain

Geometry & topology, Tome 29 (2025) no. 5, pp. 2343-2390

Résumé

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.

Détail

DOI : 10.2140/gt.2025.29.2343

Keywords: symmetric spaces, quasigeodesics, discrete subgroups

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