Homotopy truncations of homotopically stratified spaces

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

Document type :

Compte-rendu et recension critique d'ouvrage

DOI :

10.48550/arXiv.2304.14983

Title :

Homotopy truncations of homotopically stratified spaces

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 :

Proceedings of the American Mathematical Society

Publisher :

American Mathematical Society

Publication date :

2024

ISSN :

0002-9939

English keyword(s) :

Algebraic Topology (math.AT)
FOS: Mathematics
57N80
55P60
58A35
32S60

HAL domain(s) :

Mathématiques [math]

English abstract : [en]

Intersection homology of Goresky and MacPherson can be defined from the Deligne sheaf, obtained from truncations of complexes of sheaves. As intersection homology is not the homology of a particular space, the search for ...
Show more >Intersection homology of Goresky and MacPherson can be defined from the Deligne sheaf, obtained from truncations of complexes of sheaves. As intersection homology is not the homology of a particular space, the search for a family of spaces whose homologies have properties analogous to intersection homology has developed. For some stratified spaces, M. Banagl has introduced such a family by using a topological truncation: the original link is replaced by a truncation of its homological Moore resolution. In this work, we study the dual approach in the Eckmann-Hilton sense : we consider the stratified space obtained by replacing the original link by a Postnikov approximation. The main result is that our construction restores the space constructed by Gajer to establish an intersection Dold-Thom theorem. We are conducting this study within the general framework of Quinn's homotopically stratified spaces.Show less >

Language :

Anglais

Popular science :

Non

Collections :

Laboratoire Paul Painlevé - UMR 8524

Source :

Harvested from HAL

Homotopy truncations of homotopically ... BibTeX CSV Excel RIS

Homotopy truncations of homotopically ...

BibTeX

CSV

Excel

RIS