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Vanishing simplicial volume for certain affine manifolds

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NPCW05 - Group actions and cohomology in non-positive curvature

Affine manifolds, i.e. manifolds which admit charts given by affine transformations, remain mysterious by the very few  explicit examples and their famous open conjectures: the Auslander Conjecture, the Chern Conjecture and the Markus Conjecture. After reviewing the current state of knowledge on these conjectures, I will present an intermediate conjecture, somehow between the Auslander Conjecture and the Chern Conjecture, involving the simplicial volume, a topological invariant of manifolds introduced by Gromov in the beginning of the 80’s. In a joint work with Chris Connell and Jean-François Lafont, we prove the latter intermediate conjecture under some hypothesis, thus providing further evidence for the veracity of the Auslander and Chern Conjectures. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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