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Vanishing simplicial volume for certain affine manifolds

Authors: Michelle Bucher, Chris Connell and Jean-François Lafont
Journal: Proc. Amer. Math. Soc. 146 (2018), 1287-1294
MSC (2010): Primary 53A15; Secondary 57R19
Published electronically: October 10, 2017
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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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Additional Information

Michelle Bucher
Affiliation: Section de Mathematiques, Université de Genève, 2-4 rue du Livre, Case postale 64, 1211 Geneva, 4, Switzerland

Chris Connell
Affiliation: Department of Mathematics, Indiana University, 115 Rawles Hall, Bloomington, Indiana 47405

Jean-François Lafont
Affiliation: Department of Mathematics, Ohio State University, 231 W. 18th Avenue, Columbus, Ohio 43210

Received by editor(s): October 17, 2016
Received by editor(s) in revised form: April 12, 2017
Published electronically: October 10, 2017
Additional Notes: The work of the second author was partly supported by the Simons Foundation, under grant #210442
The work of the third author was partly supported by the NSF, under grant DMS-1510640.
Communicated by: Ken Bromberg
Article copyright: © Copyright 2017 American Mathematical Society

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