A cohomology attached to a function

Details A cohomology attached to a function A cohomology attached to a function

2002-12-03

arxiv.org/abs/math/0212045v1

Mathematics

Differential Geometry

18 pages

Scientific paper

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 in complex analytic geometry.

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