Volume and homology growth of aspherical manifolds

Abstract

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. Further, we show that linear growth of mod p Betti numbers or exponential growth of torsion homology imply that a closed aspherical manifold is "large".

Final version

References in corpus (1)

• Torsion homology of arithmetic lattices and K2 of imaginary fields

Cited by in corpus (3)

• Stable integral simplicial volume of 3-manifolds
• Homological growth of Artin kernels in positive characteristic
• Counting maximally broken Morse trajectories on aspherical manifolds