Modified differentials and basic cohomology for Riemannian foliations

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 Poincaré 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.

20 pages, references added, minor corrections made

References in corpus (7)

• The invertible double of elliptic operators
• The eta invariant and equivariant index of transversally elliptic operators
• A brief note on the spectrum of the basic Dirac operator
• Natural Equivariant Dirac Operators
• Rigidity of the Alvarez class
• Traces of heat operators on Riemannian foliations
• Continuity of the Alvarez class under deformations

Cited by in corpus (6)

• Index theory for basic Dirac operators on Riemannian foliations
• Exceptional complex structures and the hypermultiplet moduli of 5d Minkowski compactifications of M-theory
• Basic Dolbeault cohomology and Weitzenböck frmulas on transversely Kähler foliations
• Perturbations of basic Dirac operators on Riemannian foliations
• Transversal Dirac operators on distributions, foliations, and G-manifolds: Lecture notes
• The $S^1$-Equivariant signature for semi-free actions as an index formula