Vanishing simplicial volume for certain affine manifolds

Bucher, Michelle; Connell, Chris; Lafont, Jean-François

doi:10.1090/proc/13799

Vanishing simplicial volume for certain affine manifolds
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by Michelle Bucher, Chris Connell and Jean-François Lafont PDF

Proc. Amer. Math. Soc. 146 (2018), 1287-1294 Request permission

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. As a consequence, these manifolds have zero Euler characteristic, satisfying the Chern 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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