Abstract
(1) We provide upper bounds on the size of the homology of a closed aspherical Riemannian manifold that only depend on the systole and the volume of balls. (2) We show that linear growth of mod Betti numbers or exponential growth of torsion homology imply that a closed aspherical manifold is “large”.
Citation
Roman Sauer. "Volume and homology growth of aspherical manifolds." Geom. Topol. 20 (2) 1035 - 1059, 2016. https://doi.org/10.2140/gt.2016.20.1035
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