Modified differentials and basic cohomology for Riemannian foliations
Differential Geometry
2021-01-28 v2
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.
Cite
@article{arxiv.1007.2955,
title = {Modified differentials and basic cohomology for Riemannian foliations},
author = {Georges Habib and Ken Richardson},
journal= {arXiv preprint arXiv:1007.2955},
year = {2021}
}
Comments
20 pages, references added, minor corrections made