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Conference papers

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.
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Conference papers
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Contributor : Martintxo Saralegi-Aranguren Connect in order to contact the contributor
Submitted on : Wednesday, January 4, 2017 - 11:36:43 AM
Last modification on : Friday, January 21, 2022 - 3:30:50 AM

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  • HAL Id : hal-01426143, version 1
  • ARXIV : 1701.00684


David Chataur, Tanré Daniel, Martintxo Saralegi-Aranguren. Blown-up intersection cohomology. Rencontres doctorales Lebesgue 2016, May 2016, Rennes, France. ⟨hal-01426143⟩



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