Blown-up intersection cochains and Deligne's sheaves

David Chataur (1) , Martintxo Saralegi-Aranguren (2) , Tanré Daniel (3)

1 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352
2 LML - Laboratoire de Mathématiques de Lens
3 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: Intersection cohomology; Cap product; Cup product; Topological invariance

Domaines: Topologie algébrique [math.AT]

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⟩