Perverse homotopy groups

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

Type de document :

Pré-publication ou Document de travail

Titre :

Perverse homotopy groups

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]

Date de publication :

2022-11-11

Discipline(s) HAL :

Mathématiques [math]

Résumé en anglais : [en]

As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. ...
Lire la suite >As Goresky and MacPherson intersection homology is not the homology of a space, there is no preferred candidate for intersection homotopy groups. Here, they are defined as the homotopy groups of a simplicial set which P. Gajer associates to a couple $(X,\overline{p})$ of a filtered space and a perversity. We first establish some basic properties for the intersection fundamental groups, as a Van Kampen theorem. For general intersection homotopy groups on Siebenmann CS sets, we prove a Hurewicz theorem between them and the Goresky and MacPherson intersection homology. If the CS set and its intrinsic stratification have the same regular part, we establish the topological invariance of the $\overline{p}$-intersection homotopy groups. Several examples justify the hypotheses made in the statements. Finally, intersection homotopy groups also coincide with the homotopy groups of the topological space itself, for the top perversity on a connected, normal Thom-Mather space.Lire moins >

Langue :

Anglais

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Fichiers

2211.06096
Accès libre
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