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Modified differentials and basic cohomology for Riemannian foliations
Published 17 Jul 2010 in math.DG | (1007.2955v2)
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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