Geometry & Topology
- Geom. Topol.
- Volume 20, Number 2 (2016), 1035-1059.
Volume and homology growth of aspherical manifolds
(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”.
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
Permanent link to this document
Digital Object Identifier
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
Sauer, Roman. Volume and homology growth of aspherical manifolds. Geom. Topol. 20 (2016), no. 2, 1035--1059. doi:10.2140/gt.2016.20.1035. https://projecteuclid.org/euclid.gt/1510858972