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

@article{Fukaya2018ACC, title={A coarse Cartan–Hadamard theorem with application to the coarse Baum–Connes conjecture}, author={Tomohiro Fukaya and Shin-ichi Oguni}, journal={Journal of Topology and Analysis}, year={2018} }

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.

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