Volume and homology growth of aspherical manifolds

Sauer, Roman

doi:10.2140/gt.2016.20.1035

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Volume and homology growth of aspherical manifolds

Roman Sauer

Geometry & Topology 20 (2016) 1035–1059

DOI: 10.2140/gt.2016.20.1035

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

References

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

Volume 20, issue 2 (2016)