Curvature Operators, Laplacians, and Rational Cobordism

Abstract: We give new conditions on positivity of certain linear combinations of eigenvalues of the curvature operator of a Riemannian manifold which imply the vanishing of the indices of Dirac operators twisted with geometric vector bundles. The vanishing indices in turn have topological implications in terms of the Pontryagin classes, rational cobordism type, and Witten genus of the manifolds. To prove our results we generalize new methods developed by Petersen and Wink to apply the Bochner technique to Laplacians on geometric vector bundles.

differential geometrygeometric topologymetric geometry

Audience: researchers in the topic

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Virtual seminar on geometry with symmetries

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

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