Blown-up intersection cochains and Deligne's sheaves - Université d'Artois Access content directly
Journal Articles Geometriae Dedicata Year : 2020

Blown-up intersection cochains and Deligne's sheaves


In previous works, we have introduced the blown-up intersection cohomology and used it to extend Sullivan's minimal models theory to the framework of pseudomanifolds, and to give a positive answer to a conjecture of M. Goresky and W. Pardon on Steenrod squares in intersection homology.In this paper, we establish the main properties of this cohomology. One of its major feature is the existence of cap and cup products for any filtered space and any commutative ring of coefficients, at the cochain level. Moreover, we show that each stratified map induces an homomorphism between the blown-up intersection cohomologies, compatible with the cup and cap products. We prove also its topological invariance in the case of a pseudomanifold with no codimension one strata. Finally, we compare it with the intersection cohomology studied by G. Friedman and J.E. McClure.A great part of our results involves general perversities, defined independently on each stratum, and a tame intersection homology adapted to large perversities.
Fichier principal
Vignette du fichier
1801.02992.pdf (333.71 Ko) Télécharger le fichier
Origin : Publisher files allowed on an open archive

Dates and versions

hal-01426143 , version 1 (09-01-2024)



David Chataur, Martintxo Saralegi-Aranguren, Tanré Daniel. Blown-up intersection cochains and Deligne's sheaves. Geometriae Dedicata, 2020, 204 (1), pp.315-337. ⟨10.1007/s10711-019-00458-w⟩. ⟨hal-01426143⟩
102 View
1 Download



Gmail Facebook X LinkedIn More