Muñoz Masqué, JaimePozo Coronado, Luis Miguel2023-06-202023-06-2020121424-928610.1007/s00032-012-0173-zhttps://hdl.handle.net/20.500.14352/42396The 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.engjournal articlehttp://download.springer.com/static/pdf/961/art%253A10.1007%252Fs00032-012-0173-z.pdf?auth66=1352974245_0572dbc2a28880733879dc111e31f199&ext=.pdfhttp://www.springer.com/restricted access514515.1First integralhorizontal formsPoincare lemmasheaf cohomologysmooth foliationsRiemannian foliationsinverse problemequationsmanifoldscalculusgeometryGeometríaTopología1204 Geometría1210 Topología