Obstructions to Anosov diffeomorphisms

Date(s) : 01/07/2016
11 h 00 min - 12 h 00 min

A diffeomorphism f of a closed Riemannian manifold M is Anosov if TM has a splitting as a Whitney sum of two df-invariant subbundles, and df acts expansively on one of the subbundles, and contractively on the other.
The only known examples of manifolds supporting an Anosov map are (certain) infranilmanifolds — prompting Smale to ask whether manifolds having an Anosov diffeomorphism necessarily have to be infranil. In this talk, I will survey the known obstructions to having an Anosov diffeomorphism. I will also outline some recent work with Andrey Gogolev showing that products of certain aspherical manifolds with nilmanifolds do not support Anosov diffeomorphisms.


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