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Integral approximation of simplicial volume of graph manifolds

Graph manifolds are manifolds that decompose along tori into pieces with a tame S1 ‐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.