### Impacto

Muñoz Masqué, Jaime and Pozo Coronado, Luis Miguel
(2012)
*Cohomology of Horizontal Forms.*
Milan Journal of Mathematics, 80
(1).
pp. 169-202.
ISSN 1424-9286

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## Abstract

The complex of s-horizontal forms of a smooth foliation F on a manifold M is proved to be exact for every s = 1, . . . , n = codim F, and the cohomology groups of the complex of its global sections, are introduced. They are then compared with other cohomology groups associated to a foliation, previously introduced. An explicit formula for an s-horizontal primitive of an s-horizontal closed form, is given. The problem of representing a de Rham cohomology class by means of a horizontal closed form is analysed. Applications of these cohomology groups are included and several specific examples of explicit computation of such groups-even for non-commutative structure groups-are also presented.

Item Type: | Article |
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Uncontrolled Keywords: | First integral; horizontal forms; Poincare lemma; sheaf cohomology; smooth foliations; Riemannian foliations; inverse problem; equations; manifolds; calculus; geometry |

Subjects: | Sciences > Mathematics > Geometry Sciences > Mathematics > Topology |

ID Code: | 17107 |

Deposited On: | 15 Nov 2012 10:25 |

Last Modified: | 07 Feb 2014 09:41 |

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