Homotopie de l’espace des équivalences d’homotopie

Didierjean, Geneviève

doi:10.1090/S0002-9947-1992-0986023-2

Homotopie de l'espace des équivalences d'homotopie

Author: Geneviève Didierjean
Journal: Trans. Amer. Math. Soc. 330 (1992), 153-163
MSC: Primary 55Q52; Secondary 55P10
DOI: https://doi.org/10.1090/S0002-9947-1992-0986023-2
MathSciNet review: 986023
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Abstract: The spectral sequence of the self-fiber-homotopy-equivalences of a fibration provides a method to compute the homotopy groups of the space of self-equivalences of a space.

[1] G. Didierjean, Homotopie de l'espace des équivalences d'homotopie fibrées, Ann. Inst. Fourier (Grenoble) 35 (1985), 33-47. MR 810666 (87e:55008)
[2] P. A. Griffiths et J. W. Morgan, Rational homotopy theory and differential forms, Progr. Math. 16 (1981). MR 641551 (82m:55014)
[3] A. Legrand, Homotopie des espaces de section, Lecture Notes in Math., vol. 941, Springer-Verlag, 1981. MR 668016 (83m:55028)
[4] J. P. May, Simplicial objects in algebraic topology, Van Nostrand, 1967. MR 0222892 (36:5942)
[5] M. Mimura et N. Sawashita, On the group of self-homotopy equivalences of -spaces of rank , J. Math. Kyoto Univ. 21 (1981), 331-349. MR 625613 (82k:55009)
[6] S. Oka, On the group of self homotopy equivalences of -spaces of low rank. I, II, Mem. Fac. Sci. Kyushu Univ. Ser. A Math. 35 (1981), 247-282 et 307-323. MR 628723 (83h:55006)
[7] S. Oka, N. Sawashita, et M. Sugawara, On the group of self-equivalences of a mapping cone, Hiroshima Math. J. 4 (1974), 9-28. MR 0346779 (49:11503)
[8] J. W. Rutter, The group of homotopy self-equivalence classes of C. W. complexes, Math. Proc. Cambridge Philos. Soc. 93 (1983), 275-293. MR 691998 (84i:55002)
[9] -, The group of self-homotopy equivalences of principal three sphere bundles over the seven sphere, Math. Proc. Cambridge Philos. Soc. 78 (1978), 303-311. MR 0488039 (58:7614)
[10] N. Sawashita, On the group of self-equivalences of the product of spheres, Hiroshima Math. J. 5 (1975), 69-86. MR 0377866 (51:14035)
[11] W. Shih, On the group $\mathcal{E}(X)$ of homotopy equivalence maps, Bull. Amer. Math. Soc. 492 (1964), 361-365. MR 0160209 (28:3423)
[12] K. Tsukiyama, Self homotopy-equivalences of a space with two non-vanishing homotopy group, Proc. Amer. Math. Soc. 79 (1980), 134-138. MR 560599 (81j:55012)