Blown-up intersection cohomology

Abstract

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.

Version 1 of Arxiv 1603.08773 had been split in two parts. This is the first part (corresponding to Parts I and II of 1603.08773v1) substantially revised. The study of stratified maps in cohomology and the proof of the topological invariance have been added

Cited by in corpus (8)

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• Intersection homology duality and pairings: singular, PL, and sheaf-theoretic
• Intersection Homology. General perversities and topological invariance
• A reasonable notion of dimension for singular intersection homology
• Lefschetz duality for intersection (co)homology
• The Gysin braid for $S^3$-actions on manifolds