1996/11/23 by Jean-Paul Brasselet, Jean‐Paul Brasselet, Brasselet, Jean-Paul +2
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9611027
TeX, 16 pages
arxiv created 1996/11/23 · openalex publication_date 1996/11/23 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classical result of A. Connes asserts that the Frechet algebra of smooth functions on a smooth compact manifold X provides, by a purely algebraic procedure, the de Rham cohomology of X. Namely the procedure uses Hochschild and cyclic homology of this algebra. In the situation of a Thom-Mather stratified variety, we construct a Frechet algebra of functions on the regular part and a module of poles along the singular part. We associate to these objects a complex of differential forms and an Hochschild complex, on the regular part, both with poles along the singular part. The de Rham cohomology of the first complex and the cylic homology of the second one are related to the intersection homology of the variety, the corresponding perversity is determined by the orders of poles.