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 -manifolds and fundamental 4-forms in quaternionic manifolds are discussed.
@article{bwmeta1.element.bwnjournal-article-bcpv45i1p155bwm,
author = {Fern\'andez, Marisa and Ib\'a\~nez, Ra\'ul and de Le\'on, Manuel},
title = {The geometry of a closed form},
journal = {Banach Center Publications},
volume = {43},
year = {1998},
pages = {155-167},
zbl = {0930.53048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p155bwm}
}
Fernández, Marisa; Ibáñez, Raúl; de León, Manuel. The geometry of a closed form. Banach Center Publications, Tome 43 (1998) pp. 155-167. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv45i1p155bwm/
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