# Publishing house / Banach Center Publications / All volumes

## 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.

#### Authors

• Marisa Fernández
• Raúl Ibáñez
• Manuel de León

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