2000/07/08 by David B. Massey, Massey, David B.
Computer Science · Mathematics · Pharmacology, Toxicology and Pharmaceutics · #Advanced Combinatorial Mathematics #Alkaloids: synthesis and pharmacology #Topological and Geometric Data Analysis #math.AG #msc:32B15
paper · pdf · doi:10.48550/arxiv.math/0007047
15 pages
arxiv created 2000/07/08 · arxiv updated 2009/11/30
The characteristic cycle of a complex of sheaves on a complex analytic space provides weak information about the complex; essentially, it yields the Euler characteristics of the hypercohomology of normal data to strata. We show how perverse cohomology actually allows one to extract the individual Betti numbers of the hypercohomology of normal data to strata, not merely the Euler characteristics. We apply this to the ``calculation'' of the vanishing cycles of a complex, and relate this to the work of Parusiński and Briançon, Maisonobe, and Merle on Thom's af condition.