Geometry & Topology

A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings

Michael Kapovich, Bernhard Leeb, and Joan Porti

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We prove a Morse lemma for regular quasigeodesics in nonpositively curved symmetric spaces and euclidean buildings. We apply it to give a new coarse geometric characterization of Anosov subgroups of the isometry groups of such spaces simply as undistorted subgroups which are uniformly regular.

Article information

Geom. Topol., Volume 22, Number 7 (2018), 3827-3923.

Received: 18 February 2016
Accepted: 11 May 2018
First available in Project Euclid: 14 December 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C35: Symmetric spaces [See also 32M15, 57T15]
Secondary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 51E24: Buildings and the geometry of diagrams

symmetric spaces buildings quasigeodesics


Kapovich, Michael; Leeb, Bernhard; Porti, Joan. A Morse lemma for quasigeodesics in symmetric spaces and euclidean buildings. Geom. Topol. 22 (2018), no. 7, 3827--3923. doi:10.2140/gt.2018.22.3827.

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