# Homologie d'intersection. Perversités générales et invariance topologique.

Abstract : Topological invariance of the intersection homology of a pseudomanifold is one of the main properties of this homology. It has been first established by M. Goresky and R. MacPherson and revisited by H. King some years later, with the introduction of an intrinsic stratification, $X^*$, associated to a pseudomanifold $X$. In this work, we show that some topological invariance remains true in the case of general perversities, defined on each stratum and not only from the codimension. For doing that, we introduce in this general framework, the concept of K-perversities which correspond to GM-perversities. From a K-perversity, $\bar{p}$, on a pseudomanifold $X$, we construct a perversity, $\bar{q}$, on $X^*$ such that $H_{*}^{\overline{p}}(X)\cong H_*{\overline{q}}(X^*)$. We study also the extension of this result to a variation of intersection homology, more adapted to large perversities. \\
Mots-clés :
Type de document :
Pré-publication, Document de travail
2016

Littérature citée [13 références]

https://hal-univ-artois.archives-ouvertes.fr/hal-01272027
Contributeur : Martintxo Saralegi-Aranguren <>
Soumis le : mercredi 10 février 2016 - 09:22:57
Dernière modification le : mardi 3 juillet 2018 - 11:39:30
Document(s) archivé(s) le : samedi 12 novembre 2016 - 16:04:02

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1602.03009v1.pdf
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• HAL Id : hal-01272027, version 1

### Citation

Chataur David, Daniel Tanré, Martintxo Saralegi-Aranguren. Homologie d'intersection. Perversités générales et invariance topologique.. 2016. 〈hal-01272027〉

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