Modified differentials and basic cohomology for Riemannian foliations

Details Modified differentials and basic cohomology for Riemannian foliations Modified differentials and basic cohomology for Riemannian foliations

2010-07-17

arxiv.org/abs/1007.2955v2

Mathematics

Differential Geometry

20 pages, references added, minor corrections made

Scientific paper

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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