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Rank Rigidity for CAT(0) spaces without 3-flats

2022/12/14 by Stephan Stadler, Stadler, Stephan
Mathematics · #Geometric and Algebraic Topology #Geometric Analysis and Curvature Flows #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2212.07100

Abstract

If a group Γ acts geometrically on a CAT(0) space X without 3-flats, then either X contains a Γ-periodic geodesic which does not bound a flat half-plane, or else X is a rank 2 Riemannian symmetric space, a 2-dimensional Euclidean building or non-trivially splits as a metric product. Consequently all such groups satisfy a strong form of the Tits Alternative.

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