Geometry & Topology

Volume and homology growth of aspherical manifolds

Roman Sauer

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(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”.

Article information

Geom. Topol., Volume 20, Number 2 (2016), 1035-1059.

Received: 10 September 2014
Revised: 2 May 2015
Accepted: 9 June 2015
First available in Project Euclid: 16 November 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 20F69: Asymptotic properties of groups 57N65: Algebraic topology of manifolds

homology growth aspherical manifolds residually finite groups


Sauer, Roman. Volume and homology growth of aspherical manifolds. Geom. Topol. 20 (2016), no. 2, 1035--1059. doi:10.2140/gt.2016.20.1035.

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