Basic constructions in rational homotopy theory of function spaces
[Constructions basiques en théorie d’homotopie rationnelle des espaces fonctionnels]
Buijs, Urtzi ; Murillo, Aniceto
Annales de l'Institut Fourier, Tome 56 (2006), p. 815-838 / Harvested from Numdam
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Moyennant le foncteur de réalisation de Bousfield-Gugenheim, et à l’aide comme point de départ du modèle de Brown Szczarba d’un espace de fonctions, on décrit les objets basiques et les applications relatives au type d’homotopie rationnelle des espaces fonctionnels et de leurs composantes arc-connexes.

Via the Bousfield-Gugenheim realization functor, and starting from the Brown-Szczarba model of a function space, we give a functorial framework to describe basic objects and maps concerning the rational homotopy type of function spaces and its path components.

Publié le : 2006-01-01
DOI : https://doi.org/10.5802/aif.2201
Classification:  55P62,  54C35
Mots clés: Espace fonctionnel, modèle de Sullivan, homotopie rationnelle 
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     author = {Buijs, Urtzi and Murillo, Aniceto},
     title = {Basic constructions in rational homotopy theory of function spaces},
     journal = {Annales de l'Institut Fourier},
     volume = {56},
     year = {2006},
     pages = {815-838},
     doi = {10.5802/aif.2201},
     zbl = {1122.55008},
     mrnumber = {2244231},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2006__56_3_815_0}
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Buijs, Urtzi; Murillo, Aniceto. Basic constructions in rational homotopy theory of function spaces. Annales de l'Institut Fourier, Tome 56 (2006) pp. 815-838. doi : 10.5802/aif.2201. http://gdmltest.u-ga.fr/item/AIF_2006__56_3_815_0/

[1] Bousfield, A. K.; Gugenheim, V. K. A. M. On PL De Rham theory and rational homotopy type, Memoirs of the Amer. Math. Soc. Tome 179 (8) (1976) | MR 425956 | Zbl 0338.55008

[2] Brown, E. H.; Szczarba, R. H. Continuous cohomology and real homotopy type, Trans. Amer. Math. Soc., Tome 31 (1989), pp. 57-106 | Article | MR 929667 | Zbl 0671.55006

[3] Brown, E. H.; Szczarba, R. H. On the rational homotopy type of function spaces, Trans. Amer. Math. Soc., Tome 349 (1997), pp. 4931-4951 | Article | MR 1407482 | Zbl 0927.55012

[4] Félix, Y. Rational category of the space of sections of a nilpotent bundle, Comment. Math. Helvetici, Tome 65 (1990), pp. 615-622 | Article | MR 1078101 | Zbl 0715.55009

[5] Félix, Y.; Halperin, S.; Thomas, J.C. Rational Homotopy Theory, G.T.M., Springer, Tome 205 (2000) | MR 1802847 | Zbl 0961.55002

[6] Goerss, P. G.; Jardine, J. F. Simplicial Homotopy Theory, Progress in Mathematics, Birkhäuser, Basel-Boston-Berlin, Tome 174 (1999) | MR 1711612 | Zbl 0949.55001

[7] Haefliger, A. Rational homotopy of the space of sections of a nilpotent bundle, Trans. Amer. Math. Soc., Tome 273 (1982), pp. 609-620 | Article | MR 667163 | Zbl 0508.55019

[8] Halperin, S. Lecture on Minimal Models, Mémoires de la Société Mathématique de France Tome 230 (1983) | Numdam | Zbl 0536.55003

[9] Hilton, P.; Mislin, G.; Roitberg, J. Localization of nilpotent groups and spaces, North Holland Mathematical Studies Tome 15 (1975) (North Holland) | MR 478146 | Zbl 0323.55016

[10] Kuribayashi, K. A rational model for the evaluation map (2005) (Preprint) | Zbl 1097.18004

[11] May, J. P. Simplicial Objects in Algebraic Topology, Chicago Lectures in Mathematics (1992) (University of Chicago Press) | MR 1206474 | Zbl 0769.55001

[12] Milnor, J. On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc., Tome 342 (1994) no. 2, pp. 895-915

[13] Smith, S. Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups, Trans. Amer. Math. Soc., Tome 90 (1994), pp. 272-280 | Zbl 0802.55009

[14] Smith, S. Rational evaluation subgroups, Math. Zeit., Tome 221 (1996), pp. 387-400 | MR 1381587 | Zbl 0855.55009

[15] Sullivan, D. Infinitesimal computations in Topology, Publ. Math. de l’I.H.E.S., Tome 47 (1978), pp. 269-331 | Numdam | MR 646078 | Zbl 0374.57002

[16] Thom, R. L’homologie des espaces fonctionnels, Colloque de topologie algébrique, Centre Belge Rech. Math. (1957), pp. 29-39 | MR 89408 | Zbl 0077.36301

[17] Vigué-Poirrier, M. Sur l’homotopie rationnelle des espaces fonctionnels, Manuscripta Math., Tome 56 (1986), pp. 177-191 | Article | MR 850369 | Zbl 0597.55008