Injective models of $G$-disconnected simplicial sets

Golasiński, Marek

Annales de l'Institut Fourier, Tome 47 (1997), p. 1491-1522 / Harvested from Numdam

Résumé

Nous généralisons les résultats de G.V. Triantafillou et B. Fine sur les ensembles simpliciaux $G$-non connexes. On présente l’existence d’un modèle injectif minimal pour une ${\Bbb I}$-algèbre complète, où ${\Bbb I}$ est une $EI$-catégorie. Ensuite, nous utilisons la $EI$-catégorie ${\cal O}(G,X)$ associée à un $G$-ensemble simplicial $X$, pour appliquer ces résultats à la catégorie des $G$-ensembles simpliciaux.

Enfin, nous décrivons le $G$-type d’homotopie rationnelle d’un $G$-ensemble simplicial nilpotent en utilisant leur modèle injectif minimal

Abstract

We generalize the results by G.V. Triantafillou and B. Fine on $G$-disconnected simplicial sets. An existence of an injective minimal model for a complete ${\Bbb I}$-algebra is presented, for any $EI$-category ${\Bbb I}$. We then make use of the $EI$-category ${\cal O}(G,X)$ associated with a $G$-simplicial set $X$ to apply these results to the category of $G$-simplicial sets.

Finally, we describe the rational homotopy type of a nilpotent $G$-simplicial set by means of its injective minimal model.

Détail

Publié le : 1997-01-01

MR 99b:55020 | Zbl 0886.55012 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.1607

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