Intersection Homology. General perversities and topological invariance

Chataur, David; Saralegi-Aranguren, Martintxo; Tanré, Daniel

Document type :

Compte-rendu et recension critique d'ouvrage

Title :

Intersection Homology. General perversities and topological invariance

Author(s) :

Chataur, David [Auteur]
Laboratoire Amiénois de Mathématique Fondamentale et Appliquée - UMR CNRS 7352 UPJV [LAMFA]
Saralegi-Aranguren, Martintxo [Auteur]
Laboratoire de Mathématiques de Lens [LML]
Tanré, Daniel [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]

Journal title :

Illinois Journal of Mathematics

Publication date :

2019

HAL domain(s) :

Mathématiques [math]/Topologie algébrique [math.AT]

English abstract : [en]

Topological invariance of the intersection homology of a pseudomanifold without codimension one strata, proven by Goresky and MacPherson, is one of the main features of this homology. This property is true for strata ...
Show more >Topological invariance of the intersection homology of a pseudomanifold without codimension one strata, proven by Goresky and MacPherson, is one of the main features of this homology. This property is true for strata codimension depending perversities with some growth conditions, verifying $\overline p(1)=\overline p(2)=0$. King reproves this invariance by associating an intrinsic pseudomanifold $X^*$ to any pseudomanifold $X$. His proof consists of an isomorphism between the associated intersection homologies $H^{\overline{p}}_{*}(X) \cong H^{\overline{p}}_{*}(X^*)$ for any perversity $\overline{p}$ with the same growth conditions verifying $\overline p(1)\geq 0$. In this work, we prove a certain topological invariance within the framework of strata depending perversities, $\overline{p}$, which corresponds to the classical topological invariance if $\overline{p}$ is a GM-perversity. We also extend it to the tame intersection homology, a variation of the intersection homology, particularly suited for "large" perversities, if there is no singular strata on $X$ becoming regular in $X^*$. In particular, under the above conditions, the intersection homology and the tame intersection homology are invariant under a refinement of the stratification.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Files

1602.03009
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