Abstract
In 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 [Compositio Math. 76 (1990) 19–47] in complex analytic geometry.
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