Riemannian Topology Meeting

8-9 November 2018
University of Fribourg, Switzerland
Europe/Berlin timezone

Positively curved manifolds with isometric torus actions

9 Nov 2018, 14:30
50m
University of Fribourg, Switzerland

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 $\mathbb{H} P^{n/4}$.

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