A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture

Abstract

We establish a coarse version of the Cartan-Hadamard theorem, which states that proper coarsely convex spaces are coarsely homotopy equivalent to the open cones of their ideal boundaries. As an application, we show that such spaces satisfy the coarse Baum-Connes conjecture. Combined with the result of Osajda-Przytycki, it implies that systolic groups and locally finite systolic complexes satisfy the coarse Baum-Connes conjecture.

v.2 34 pages, added Section 7 on groups acting on a coarsely convex space. v.3 38 pages, added Section 8 on a functional analytic characterization of ideal boundaries

References in corpus (1)

• Coronae of product spaces and the Coarse Baum-Connes conjecture

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