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A Morse Lemma for quasigeodesics in symmetric spaces and euclidean buildings


Speaker: Bernhard Leeb, LMU Munchen
Location: 2112 MSB
Start time: Tue, Nov 25 2014, 3:10PM

We prove a Morse Lemma for coarsely regular quasigeodesics in nonpositively curved symmetric spaces and euclidean buildings X. The main application is a simpler coarse geometric characterization of Morse subgroups of the isometry groups Isom(X) as undistorted subgroups which are coarsely uniformly regular. We show furthermore that they must be word hyperbolic. We introduced this class of discrete subgroups in our earlier work, in the context of symmetric spaces, where various equivalent geometric and dynamical characterizations of word hyperbolic Morse subgroups were established, including the Anosov subgroup property. This is a joint work with Misha Kapovich and Joan Porti.