Intersection Homology. General perversities and topological invariance
Résumé
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.
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Origine : Fichiers produits par l'(les) auteur(s)
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