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
Full-text PDF
Abstract | References | Similar Articles | Additional Information
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
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)
Retrieve articles in Transactions of the American Mathematical Society with MSC: 55Q52, 55P10
Retrieve articles in all journals with MSC: 55Q52, 55P10
Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1992-0986023-2
Article copyright:
© Copyright 1992
American Mathematical Society