2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65873In this paper, we study a certain cohomology attached to a smooth function, which arose naturally in Poisson geometry. We explain how this cohomology depends on the function, and we prove that it satisfies both the excision and the Mayer-Vietoris axioms. For a regular function we show that the cohomology is related to the de Rham cohomology. Finally, we use it to give a new proof of a well-known result of A. Dimca in complex analytic geometry.18 pagesDifferential Geometry53D17, 58A10, 14F40, 32S05text