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Séminaire Géométrie et groupes discrets

Vanishing simplicial volume for certain affine manifolds

by Prof. Michelle BUCHER (Université de Genève)

lundi 16 octobre 2017 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
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. I will discuss an intermediate conjecture, somehow between the Auslander Conjecture and the Chern Conjecture, predicting the vanishing of the simplicial volume of affine manifolds. In a joint work with Chris Connell and Jean-François Lafont, we prove the latter conjecture under some hypothesis, thus providing further evidence for the veracity of the Auslander and Chern Conjectures. To do so, we provide a simple cohomological criterion for aspherical manifolds with normal amenable subgroups in their fundamental group to have vanishing simplicial volume. This answers a special case of a question due to Lück. 
Joint work with Chris Connell and Jean-François Lafont.

Organisé par Fanny Kassel
Contact Email: cecile@ihes.fr