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Dans le fibre de l’espace des lacets libres, la fibre n’est pas, en général, totalement non cohomologue à zéro. (French) Zbl 0505.55006

MSC:
55P35 Loop spaces
55P62 Rational homotopy theory
55P60 Localization and completion in homotopy theory
53C22 Geodesics in global differential geometry
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References:
[1] Gromov, M.: Homotopical effects of dilatation. J. Differential Geometry13, 303-310 (1978) · Zbl 0427.58010
[2] Grove, K., Halperin, S., Vigué-Poirrier, M.: The rational homotopy theory of certain path spaces with applications to geodesics. Acta Math.140, 277-303 (1978) · Zbl 0421.58007 · doi:10.1007/BF02392310
[3] Halperin, S.: Lectures on mimimal models. Publications internes de l’U.E.R. de Mathématiques Pures de l’Université de Lille I, Vol.111 (1977)
[4] Halperin, S.: Rational Fibrations, minimal models, and fibrings of homogeneous spaces. Trans. Amer. Math. Soc.244, 199-223 (1978) · Zbl 0387.55010 · doi:10.1090/S0002-9947-1978-0515558-4
[5] Halperin, S., Stasheff, J.: Obstructions to homotopy equivalence. Advances in Math.32, 233-279 (1979) · Zbl 0408.55009 · doi:10.1016/0001-8708(79)90043-4
[6] Smith, L.: On the characteristic zero cohomology of the free loop space. Amer. J. Math.103, 887-910 (1981) · Zbl 0475.55004 · doi:10.2307/2374251
[7] Sullivan, D.: Infinitesimal computations in topology. Inst. Hautes Etudes Sci. Publ. Math.47, (1977) · Zbl 0374.57002
[8] Sullivan, D., Vigué-Poirrier, M.: The homology theory of the closed geodesic problem. J. Differential Geometry11, 633-644 (1976) · Zbl 0361.53058
[9] Thomas, J.C.: Rational homotopy of Serre fibrations. Annales Inst. Fourier (Grenoble)31, 71-90 (1981) · Zbl 0446.55009
[10] Vigué-Poirrier, M.: Réalisation de morphismes donnés en cohomologie et suite spectrale d’Eilenberg-Moore. Trans. Amer. Math. Soc.265, 447-484 (1981) · Zbl 0474.55009
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