A reasonable notion of dimension for singular intersection homology

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

Type de document :

Article dans une revue scientifique: Article original

DOI :

10.1007/s40062-024-00343-8

URL permanente :

http://hdl.handle.net/20.500.12210/121308

Titre :

A reasonable notion of dimension for singular intersection homology

Auteur(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]

Titre de la revue :

Journal of Homotopy and Related Structures

Éditeur :

Springer

Date de publication :

2024-04-04

ISSN :

2193-8407

Mot(s)-clé(s) en anglais :

Intersection homology
Topological invariance
Pseudo-barycentric subdivision

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula to make selections among singular simplexes. This formula needs a notion ...
Lire la suite >M. Goresky and R. MacPherson intersection homology is also defined from the singular chain complex of a filtered space by H. King, with a key formula to make selections among singular simplexes. This formula needs a notion of dimension for subspaces S of an Euclidean simplex, which is usually taken as the smallest dimension of the skeleta containing S. Later, P. Gajer employed another dimension based on the dimension of polyhedra containing S. This last one allows traces of pullbacks of singular strata in the interior of the domain of a singular simplex. In this work, we prove that the two corresponding intersection homologies are isomorphic for Siebenmann's CS sets. In terms of King's paper, this means that polyhedral dimension is a "reasonable" dimension. The proof uses a Mayer-Vietoris argument which needs an adapted subdivision. With the polyhedral dimension, that is a subtle issue. General position arguments are not sufficient and we introduce strong general position. With it, a stability is added to the generic character and we can do an inductive cutting of each singular simplex. This decomposition is realised with pseudo-barycentric subdivisions where the new vertices are not barycentres but close points of them.Lire moins >

Langue :

Anglais

Comité de lecture :

Oui

Audience :

Internationale

Vulgarisation :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Date de dépôt :

2025-01-24T13:38:11Z

Fichiers

2211.06090
Accès libre
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