Vanishing simplicial volume for certain affine manifolds
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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 $\pi_1$ to have vanishing simplicial volume. This answers a special case of a question due to Lück.
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Bucher, Michelle, et al. "Vanishing simplicial volume for certain affine manifolds." Proceedings of the American Mathematical Society, vol. 146, no. 3, pp. 1287--1294, 2018, https://doi.org/10.1090/proc/13799.
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Proceedings of the American Mathematical Society
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