The geometry of a closed form
Volume 45 / 1998
Banach Center Publications 45 (1998), 155-167
DOI: 10.4064/-45-1-155-167
Abstract
It is proved that a closed r-form ω on a manifold M defines a cohomology (called ω-coeffective) on M. A general algebraic machinery is developed to extract some topological information contained in the ω-coeffective cohomology. The cases of 1-forms, symplectic forms, fundamental 2-forms on almost contact manifolds, fundamental 3-forms on $G_{2}$-manifolds and fundamental 4-forms in quaternionic manifolds are discussed.
