Speaker
Michael Wiemeler
(WWU Münster)
Description
The classification of positively (sectional) curved manifolds is a long standing open problem in Riemannian geometry. So far it was a successful approach to consider the problem under the extra assumption of an isometric group action.
In this talk I will report on recent joint work with Lee Kennard and Burkhard Wilking in this direction. Among other things we show the following: Let $M$ be a simply connected positively curved $n$-dimensional manifold with $H^{odd} M,\mathbb{Q})=0$ and an isometric $T^8$-action. Then the rational cohomology ring of $M$ is isomorphic to the rational cohomology of one of the CROSSes $S^n$, $\mathbb{C} P^{n/2}$ and $\mathbb{H} P^{n/4}$.
