New Curvature Conditions for the Bochner Technique

Abstract: The Bochner Technique has established itself as a powerful tool in Geometry, e.g.\ D.~Meyer used it to show that the Betti numbers $b_p$ of compact $n$-dimensional manifolds with positive curvature operators vanish for $0 < p < n$. In this talk I will explain that this is more generally the case for manifolds with $\lceil \frac{n}{2} \rceil$-positive curvature operators. We will see that this is a consequence of a general vanishing and estimation theorem for the $p$-th Betti number for manifolds with a lower bound on the average of the lowest $(n-p)$ eigenvalues of the curvature operator. This talk is based on joint work with Peter Petersen.

differential geometry

Audience: researchers in the topic

( video )

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Virtual seminar on geometry with symmetries

Series comments: Description: Research seminar in Lie group actions in Riemannian geometry.

The seminar meets every other Wednesday. To accommodate most time zones, the time rotates. The Zoom link is sent to the mailing list around 24 hours before each talk. To subscribe to the mailing list, send a message to geometrywithsymmetries@gmail.com requiring it.

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