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arXiv · 1007.2955

Modified differentials and basic cohomology for Riemannian foliations

Georges Habib·Ken Richardson
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Abstract

We define a new version of the exterior derivative on the basic forms of a Riemannian foliation to obtain a new form of basic cohomology that satisfies Poincar\'e duality in the transversally orientable case. We use this twisted basic cohomology to show relationships between curvature, tautness, and vanishing of the basic Euler characteristic and basic signature.

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Georges Habib, Ken Richardson. 2010-07-17. Modified differentials and basic cohomology for Riemannian foliations. https://doi.org/10.1007/s12220-011-9289-6

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