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Search: MSC category 18G55 ( Homotopical algebra )

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1. CMB 2001 (vol 44 pp. 459)

Kahl, Thomas
LS-catégorie algébrique et attachement de cellules
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
Categories:55M30, 18G55

2. CMB 2000 (vol 43 pp. 162)

Foth, Philip
Moduli Spaces of Polygons and Punctured Riemann Spheres
The purpose of this note is to give a simple combinatorial construction of the map from the canonically compactified moduli spaces of punctured complex projective lines to the moduli spaces $\P_r$ of polygons with fixed side lengths in the Euclidean space $\E^3$. The advantage of this construction is that one can obtain a complete set of linear relations among the cycles that generate homology of $\P_r$. We also classify moduli spaces of pentagons.

Categories:14D20, 18G55, 14H10

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