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LS-catégorie algébrique et attachement de cellules

Published online by Cambridge University Press:  20 November 2018

Thomas Kahl
Thomas Kahl*
Affiliation:
UMR CNRS 8524 U.F.R. de Mathématiques Université des Sciences et Technologies de Lille 59655 Villeneuve d’Ascq Cedex France, courriel: kahl@agat.univ-lille1.fr
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Résumé

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Nous montrons que la $\text{A}$-catégorie d’un espace simplement connexe de type fini est inférieure ou égale à $n$ si et seulement si son modèle d’Adams-Hilton est un rétracte homotopique d’une algèbre différentielle à $n$ étages. Nous en déduisons que l’invariant Acat augmente au plus de 1 lors de l’attachement d’une cellule à un espace.

Abstract

Abstract

We show that the $\text{A}$-category of a simply connected space of finite type is less than or equal to $n$ if and only if its Adams-Hilton model is a homotopy retract of an $n$-stage differential algebra. We deduce from this that the invariant Acat increases by at most 1 when a cell is attached to a space.

Keywords

55M3018G55LS-categorystrong categoryAdams-Hilton modelscell attachments
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 44 , Issue 4 , 01 December 2001 , pp. 459 - 468
Copyright
Copyright © Canadian Mathematical Society 2001

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