The geometry of a closed form

Volume 45 / 1998

Marisa Fernández, Raúl Ibáñez, Manuel de León Banach Center Publications 45 (1998), 155-167 DOI: 10.4064/-45-1-155-167


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.


  • Marisa Fernández
  • Raúl Ibáñez
  • Manuel de León

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