Nous généralisons les résultats de G.V. Triantafillou et B. Fine sur les ensembles simpliciaux -non connexes. On présente l’existence d’un modèle injectif minimal pour une -algèbre complète, où est une -catégorie. Ensuite, nous utilisons la -catégorie associée à un -ensemble simplicial , pour appliquer ces résultats à la catégorie des -ensembles simpliciaux.
Enfin, nous décrivons le -type d’homotopie rationnelle d’un -ensemble simplicial nilpotent en utilisant leur modèle injectif minimal
We generalize the results by G.V. Triantafillou and B. Fine on -disconnected simplicial sets. An existence of an injective minimal model for a complete -algebra is presented, for any -category . We then make use of the -category associated with a -simplicial set to apply these results to the category of -simplicial sets.
Finally, we describe the rational homotopy type of a nilpotent -simplicial set by means of its injective minimal model.
@article{AIF_1997__47_5_1491_0, author = {Golasi\'nski, Marek}, title = {Injective models of $G$-disconnected simplicial sets}, journal = {Annales de l'Institut Fourier}, volume = {47}, year = {1997}, pages = {1491-1522}, doi = {10.5802/aif.1607}, mrnumber = {99b:55020}, zbl = {0886.55012}, language = {en}, url = {http://dml.mathdoc.fr/item/AIF_1997__47_5_1491_0} }
Golasiński, Marek. Injective models of $G$-disconnected simplicial sets. Annales de l'Institut Fourier, Tome 47 (1997) pp. 1491-1522. doi : 10.5802/aif.1607. http://gdmltest.u-ga.fr/item/AIF_1997__47_5_1491_0/
[1] On PL de Rham theory and rational homotopy type, Memories Amer. Math. Soc., 179 (1976). | MR 54 #13906 | Zbl 0338.55008
and ,[2] Equivariant Cohomology Theories, Lecture Notes in Math., Springer-Verlag, 34 (1967). | MR 35 #4914 | Zbl 0162.27202
,[3] System of fixed point sets, Trans. Amer. Math. Soc., 277 (1983), 275-284. | MR 84f:57029 | Zbl 0521.57027
,[4] Disconnected equivariant rational homotopy theory and formality of compact G-Kähler manifolds, Ph. D. thesis, Chicago 1992.
,[5] On the equivariant formality of Kähler manifolds with finite group action, Can. J. Math., 45 (1993), 1200-1210. | MR 94j:55010 | Zbl 0805.55009
and ,[6] Injectivity of the de Rham algebra on G-disconnected simplicial sets, (submitted).
,[7] Equivariant Rational Homotopy Theory as a Closed Model Category, J. Pure Appl. Alg., (to appear). | Zbl 0929.55012
,[8] Componentwise injective models of functors to DGAs, Colloq. Math., 73 (1997), 83-92. | MR 98b:55012 | Zbl 0877.55004
,[9] Lectures on minimal models, Mémories S.M.F., nouvelle série, 9-10 (1983). | Numdam | MR 85i:55009 | Zbl 0536.55003
,[10] Algebraic topology, Amer. Math. Soc. Colloq. Publ., XXVII (1942). | MR 4,84f | Zbl 0061.39302
,[11] Transformation groups and Algebraic K-Theory, Lect. Notes in Math., Springer-Verlag, 1408 (1989). | MR 91g:57036 | Zbl 0679.57022
,[12] Infinitesimal Computations in Topology, Publ. Math. I.H.E.S., 47 (1977), 269-331. | Numdam | MR 58 #31119 | Zbl 0374.57002
,[13] Equivariant minimal models, Trans. Amer. Math. Soc., 274 (1982), 509-532. | MR 84g:55017 | Zbl 0516.55010
,[14] Ratinalization of Hopf G-spaces, Math. Z., 182 (1983), 485-500. | MR 84h:55008 | Zbl 0518.55008
,[15] An algebraic model for G-homotopy types, Astérisque, 113-114 (1984), 312-337. | MR 85m:55009 | Zbl 0564.55009
,