Abstract:
In this paper we study a basic cohomology attached to a basic function of foliated manifolds and in particular, of transversely holomorphic foliations. We also explain how this cohomology depends on the basic function and we study a relative cohomology and a Mayer-Vietoris sequence related to this cohomology. Also, a basic Lichnerowicz cohomology attached to a basic function of a foliated manifold is studied.
Keywords and phrases:foliated manifolds, basic forms, cohomology.
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