Geometry & Topology

Volume and homology growth of aspherical manifolds

Roman Sauer

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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”.

Article information

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

Dates
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
https://projecteuclid.org/euclid.gt/1510858972

Digital Object Identifier
doi:10.2140/gt.2016.20.1035

Mathematical Reviews number (MathSciNet)
MR3493098

Zentralblatt MATH identifier
1338.53067

Subjects
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

Keywords
homology growth aspherical manifolds residually finite groups

Citation

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


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