Poincaré duality with cap products in intersection homology

Abstract : For having a Poincaré duality via a cap product between the intersection homology of a paracompact oriented pseudomanifold and the cohomology given by the dual complex, G. Friedman and J. E. McClure need a coefficient field or an additional hypothesis on the torsion. In this work, by using the classical geometric process of blowing-up, adapted to a simplicial setting, we build a cochain complex which gives a Poincaré duality via a cap product with intersection homology, for any commutative ring of coefficients. We prove also the topological invariance of the blown-up intersection cohomology with compact supports in the case of a paracompact pseudomanifold with no codimension one strata. This work is written with general perversities, defined on each stratum and not only in function of the codimension of strata. It contains also a tame intersection homology, suitable for large perversities.
Document type :
Journal articles
Complete list of metadatas

https://hal-univ-artois.archives-ouvertes.fr/hal-01427131
Contributor : Martintxo Saralegi-Aranguren <>
Submitted on : Thursday, January 5, 2017 - 12:23:15 PM
Last modification on : Sunday, April 28, 2019 - 10:25:22 AM
Long-term archiving on : Thursday, April 6, 2017 - 1:09:13 PM

File

ArxivJanvier2017.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01427131, version 1

Collections

Citation

David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré. Poincaré duality with cap products in intersection homology. Advances in Mathematics, Elsevier, 2018, 326, pp.314-351. ⟨hal-01427131⟩

Share

Metrics

Record views

397

Files downloads

448