Vanishing simplicial volume for certain affine manifolds
Abstract
We show that closed aspherical manifolds supporting an affine structure, whose holonomy map is injective and contains a pure translation, must have vanishing simplicial volume. This provides some further evidence for the veracity of the Auslander Conjecture. Along the way, we provide a simple cohomological criterion for aspherical manifolds with normal amenable subgroups of π1 to have vanishing simplicial volume. This answers a special case of a question due to L\"uck.
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