Intersection Homology. General perversities ...
Document type :
Article dans une revue scientifique: Article original
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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]
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
English keyword(s) :
CS-set
Intrinsic CS-set
Pseudomanifold
and phrases Intersection homology
Perversity
Intersection homology
Perversiy
Intrinsic CS set
CS set
Topological Invariance
Intrinsic CS-set
Pseudomanifold
and phrases Intersection homology
Perversity
Intersection homology
Perversiy
Intrinsic CS set
CS set
Topological Invariance
HAL domain(s) :
Mathématiques [math]/Topologie algébrique [math.AT]
English abstract : [en]
Topological invariance of the intersection homology of a pseudomanifold isone of the main properties of this homology. It has been first established byM. Goresky and R. MacPherson and revisited by H. King some years later, ...
Show more >Topological invariance of the intersection homology of a pseudomanifold isone of the main properties of this homology. It has been first established byM. Goresky and R. MacPherson and revisited by H. King some years later, withthe introduction of an intrinsic stratification, $X^*$, associated to apseudomanifold $X$. In this work, we show that some topological invariance remains true in thecase of general perversities, defined on each stratum and not only from thecodimension. For doing that, we introduce in this general framework, theconcept of K-perversities which correspond to GM-perversities. From aK-perversity, $\bar{p}$, on a pseudomanifold $X$, we construct a perversity,$\bar{q}$, on $X^*$ such that $H_{*}^{\overline{p}}(X)\congH_*{\overline{q}}(X^*)$. We study also the extension of this result to avariation of intersection homology, more adapted to large perversities.\\Show less >
Show more >Topological invariance of the intersection homology of a pseudomanifold isone of the main properties of this homology. It has been first established byM. Goresky and R. MacPherson and revisited by H. King some years later, withthe introduction of an intrinsic stratification, $X^*$, associated to apseudomanifold $X$. In this work, we show that some topological invariance remains true in thecase of general perversities, defined on each stratum and not only from thecodimension. For doing that, we introduce in this general framework, theconcept of K-perversities which correspond to GM-perversities. From aK-perversity, $\bar{p}$, on a pseudomanifold $X$, we construct a perversity,$\bar{q}$, on $X^*$ such that $H_{*}^{\overline{p}}(X)\congH_*{\overline{q}}(X^*)$. We study also the extension of this result to avariation of intersection homology, more adapted to large perversities.\\Show less >
Language :
Français
Peer reviewed article :
Oui
Audience :
Internationale
Popular science :
Non
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Source :
Submission date :
2025-01-24T17:29:32Z
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