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Cohomology of Horizontal Forms

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
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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