2002/12/03 by Philippe Monnier, Monnier, Philippe
Mathematics · #14F40 #32S05 #53D17 #58A10 #Differential Geometry (math.DG) #FOS: Mathematics #math.DG #msc:14F40 #msc:32S05 #msc:53D17 #msc:58A10
paper · pdf · doi:10.48550/arxiv.math/0212045
18 pages
arxiv created 2002/12/03 · arxiv updated 2009/11/30
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.