Integral approximation of simplicial volume of graph manifolds

Abstract

Graph manifolds are manifolds that decompose along tori into pieces with a tame $S^1$-structure. In this paper, we prove that the simplicial volume of graph manifolds (which is known to be zero) can be approximated by integral simplicial volumes of their finite coverings. This gives a uniform proof of the vanishing of rank gradients, Betti number gradients and torsion homology gradients for graph manifolds.

arXiv comment18 pages

References in corpus (3)

• Stable complexity and simplicial volume of manifolds
• Rigidity of high dimensional graph manifolds
• Integral foliated simplicial volume and $S^1$-actions

Cited by in corpus (7)

• Stable integral simplicial volume of 3-manifolds
• A Matsumoto-Mostow result for Zimmer's cocycles of hyperbolic lattices
• On the simplicial volume and the Euler characteristic of (aspherical) manifolds
• Multiplicative constants and maximal measurable cocycles in bounded cohomology
• Integral foliated simplicial volume and circle foliations
• A note on $p$-adic simplicial volumes
• Simplicial volume with ${\mathbb{F}}_p$-coefficients