#### Volume 20, issue 2 (2016)

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Volume and homology growth of aspherical manifolds

### Roman Sauer

Geometry & Topology 20 (2016) 1035–1059
##### 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 $p$ Betti numbers or exponential growth of torsion homology imply that a closed aspherical manifold is “large”.

##### Keywords
homology growth, aspherical manifolds, residually finite groups
##### Mathematical Subject Classification 2010
Primary: 53C23
Secondary: 20F69, 57N65
##### Publication
Received: 10 September 2014
Revised: 2 May 2015
Accepted: 9 June 2015
Published: 28 April 2016
Proposed: Benson Farb
Seconded: Dmitri Burago, Martin Robert Bridson
##### Authors
 Roman Sauer Fakultät für Mathematik Karlsruhe Institute of Technology Institut für Algebra und Geometrie (IAG), AG Topologie Englerstr. 2 D-76131 Karlsruhe Germany