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LS-catégorie algébrique et attachement de cellules

  Published:2001-12-01
 Printed: Dec 2001
  • Thomas Kahl
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Abstract

Nous montrons que la A-cat\'egorie d'un espace simplement connexe de type fini est inf\'erieure ou \'egale \`a $n$ si et seulement si son mod\`ele d'Adams-Hilton est un r\'etracte homotopique d'une alg\`ebre diff\'erentielle \`a $n$ \'etages. Nous en d\'eduisons que l'invariant $\Acat$ augmente au plus de 1 lors de l'attachement d'une cellule \`a un espace. We show that the 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: LS-category, strong category, Adams-Hilton models, cell attachments LS-category, strong category, Adams-Hilton models, cell attachments
MSC Classifications: 55M30, 18G55 show english descriptions Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
Homotopical algebra
55M30 - Ljusternik-Schnirelman (Lyusternik-Shnirel'man) category of a space
18G55 - Homotopical algebra
 

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