English

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.

Keywords

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

R2 v1 2026-06-21T15:49:21.731Z