Intersection Homology. General perversities and topological invariance

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. \\
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David Chataur, Martintxo Saralegi-Aranguren, Daniel Tanré. Intersection Homology. General perversities and topological invariance. Illinois Journal of Mathematics, A paraître. ⟨hal-01272027v2⟩

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