[Constructions basiques en théorie d’homotopie rationnelle des espaces fonctionnels]
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.
Keywords: Function space, mapping space, Sullivan model, rational homotopy theory
Mot clés : Espace fonctionnel, modèle de Sullivan, homotopie rationnelle
@article{AIF_2006__56_3_815_0,
author = {Buijs, Urtzi and Murillo, Aniceto},
title = {Basic constructions in rational homotopy theory of function spaces},
journal = {Annales de l'Institut Fourier},
pages = {815--838},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {56},
number = {3},
year = {2006},
doi = {10.5802/aif.2201},
zbl = {1122.55008},
mrnumber = {2244231},
language = {en},
url = {https://www.numdam.org/articles/10.5802/aif.2201/}
}
TY - JOUR AU - Buijs, Urtzi AU - Murillo, Aniceto TI - Basic constructions in rational homotopy theory of function spaces JO - Annales de l'Institut Fourier PY - 2006 SP - 815 EP - 838 VL - 56 IS - 3 PB - Association des Annales de l’institut Fourier UR - https://www.numdam.org/articles/10.5802/aif.2201/ DO - 10.5802/aif.2201 LA - en ID - AIF_2006__56_3_815_0 ER -
%0 Journal Article %A Buijs, Urtzi %A Murillo, Aniceto %T Basic constructions in rational homotopy theory of function spaces %J Annales de l'Institut Fourier %D 2006 %P 815-838 %V 56 %N 3 %I Association des Annales de l’institut Fourier %U https://www.numdam.org/articles/10.5802/aif.2201/ %R 10.5802/aif.2201 %G en %F AIF_2006__56_3_815_0
Buijs, Urtzi; Murillo, Aniceto. Basic constructions in rational homotopy theory of function spaces. Annales de l'Institut Fourier, Tome 56 (2006) no. 3, pp. 815-838. doi : 10.5802/aif.2201. https://www.numdam.org/articles/10.5802/aif.2201/
[1] On PL De Rham theory and rational homotopy type, 179 (8), Memoirs of the Amer. Math. Soc., 1976 | MR | Zbl
[2] Continuous cohomology and real homotopy type, Trans. Amer. Math. Soc., Volume 31 (1989), pp. 57-106 | DOI | MR | Zbl
[3] On the rational homotopy type of function spaces, Trans. Amer. Math. Soc., Volume 349 (1997), pp. 4931-4951 | DOI | MR | Zbl
[4] Rational category of the space of sections of a nilpotent bundle, Comment. Math. Helvetici, Volume 65 (1990), pp. 615-622 | DOI | MR | Zbl
[5] Rational Homotopy Theory, G.T.M., Volume 205, Springer, 2000 | MR | Zbl
[6] Simplicial Homotopy Theory, Progress in Mathematics, Volume 174, Birkhäuser, Basel-Boston-Berlin, 1999 | MR | Zbl
[7] Rational homotopy of the space of sections of a nilpotent bundle, Trans. Amer. Math. Soc., Volume 273 (1982), pp. 609-620 | DOI | MR | Zbl
[8] Lecture on Minimal Models, 230, Mémoires de la Société Mathématique de France, 1983 | Numdam | Zbl
[9] Localization of nilpotent groups and spaces, 15, North Holland Mathematical Studies, 1975 (North Holland) | MR | Zbl
[10] A rational model for the evaluation map (2005) (Preprint) | Zbl
[11] Simplicial Objects in Algebraic Topology, Chicago Lectures in Mathematics, 1992 (University of Chicago Press) | MR | Zbl
[12] On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc., Volume 342 (1994) no. 2, pp. 895-915
[13] Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups, Trans. Amer. Math. Soc., Volume 90 (1994), pp. 272-280 | Zbl
[14] Rational evaluation subgroups, Math. Zeit., Volume 221 (1996), pp. 387-400 | MR | Zbl
[15] Infinitesimal computations in Topology, Publ. Math. de l’I.H.E.S., Volume 47 (1978), pp. 269-331 | Numdam | MR | Zbl
[16] L’homologie des espaces fonctionnels, Colloque de topologie algébrique, Centre Belge Rech. Math. (1957), pp. 29-39 | MR | Zbl
[17] Sur l’homotopie rationnelle des espaces fonctionnels, Manuscripta Math., Volume 56 (1986), pp. 177-191 | DOI | MR | Zbl
- Cartan calculi on the free loop spaces, Journal of Pure and Applied Algebra, Volume 228 (2024) no. 11, p. 107708 | DOI:10.1016/j.jpaa.2024.107708
- On the scanning map and the space of smooth complex projective hypersurfaces, The Quarterly Journal of Mathematics, Volume 75 (2024) no. 4, p. 1507 | DOI:10.1093/qmath/haae056
- Characteristic classes for families of bundles, Selecta Mathematica, Volume 28 (2022) no. 3 | DOI:10.1007/s00029-022-00764-4
- Rational model for the string coproduct of pure manifolds, Journal of Homotopy and Related Structures, Volume 16 (2021) no. 4, p. 667 | DOI:10.1007/s40062-021-00293-5
- The homotopy fixed point set of Lie group actions on elliptic spaces, Proceedings of the London Mathematical Society, Volume 110 (2015) no. 5, p. 1135 | DOI:10.1112/plms/pdv015
- Evaluation Fibrations and Path-Components of the Mapping Space
- Algebraic models of non-connected spaces and homotopy theory ofL∞algebras, Advances in Mathematics, Volume 236 (2013), p. 60 | DOI:10.1016/j.aim.2012.12.014
- An explicit L∞ structure for the components of mapping spaces, Topology and its Applications, Volume 159 (2012) no. 3, p. 721 | DOI:10.1016/j.topol.2011.11.030
- On extensions of a symplectic class, Differential Geometry and its Applications, Volume 29 (2011) no. 6, p. 801 | DOI:10.1016/j.difgeo.2011.08.008
- Rational homotopy of gauge groups, Proceedings of the American Mathematical Society, Volume 137 (2008) no. 4, p. 1519 | DOI:10.1090/s0002-9939-08-09721-9
Cité par 10 documents. Sources : Crossref
