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oai:docta.ucm.es:20.500.14352/423962023-08-27T16:51:56Zcom_20.500.14352_14col_20.500.14352_15

Cohomology of Horizontal Forms Muñoz Masqué, Jaime Pozo Coronado, Luis Miguel 514 515.1 First integral horizontal forms Poincare lemma sheaf cohomology smooth foliations Riemannian foliations inverse problem equations manifolds calculus geometry Geometría Topología 1204 Geometría 1210 Topología 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. MICINN Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T00:19:26Z 2023-06-20T00:19:26Z 2012 journal article https://hdl.handle.net/20.500.14352/42396 1424-9286 10.1007/s00032-012-0173-z eng MTM2008-01386 restricted access application/pdf Birkhäuser