Homotopy Invariants and almost non-negative curvature

Abstract: Almost non-negative sectional curvature (ANSC) is a curvature condition on a Riemannian manifold, which encompasses both the almost flat and the non-negatively curved case. It was shown in a remarkable paper by Kapovitch, Petrunin and Tuschmann that, modulo some technical details, a compact ANSC manifold is a fiber bundle over a nilmanifold, and that the fiber satisfies a curvature condition only slightly more general than ANSC. In this talk, based on joint work with G. Lupton and J. Oprea, we will discuss such manifolds from the point of view of Rational Homotopy Theory, presenting various invariants of bundles of such type, and proving a (rational) Bochner-type theorem.

Mathematics

Audience: researchers in the topic

Geometry Seminar - University of Florence

Series comments: If you are interested in attending, please send a message to daniele.angella@unifi.it or francesco.pediconi@unifi.it.