Un des problèmes historiques de la théorie homotopique des espaces est de mesurer l’effet de l’attachement d’une cellule au niveau des groupes d’homotopie. Le problème de l’attachement inerte reste en particulier un problème ouvert. Nous donnons ici une réponse partielle à ce problème.
One of the historical problem in homotopy theory consists to measure the effect of adding a cell in the homotopy groups. In particular, the problem of inert attachment remains an open problem. We give here a partial answer to this question.
@article{AIF_1989__39_1_207_0,
author = {F\'elix, Yves and Thomas, Jean-Claude},
title = {Effet d'un attachement cellulaire dans l'homologie de l'espace des lacets},
journal = {Annales de l'Institut Fourier},
volume = {39},
year = {1989},
pages = {207-224},
doi = {10.5802/aif.1164},
mrnumber = {90j:55012},
zbl = {0686.55005},
language = {fr},
url = {http://dml.mathdoc.fr/item/AIF_1989__39_1_207_0}
}
Félix, Yves; Thomas, Jean-Claude. Effet d'un attachement cellulaire dans l'homologie de l'espace des lacets. Annales de l'Institut Fourier, Tome 39 (1989) pp. 207-224. doi : 10.5802/aif.1164. http://gdmltest.u-ga.fr/item/AIF_1989__39_1_207_0/
[1] et , On the chain algebra of a loop space, Comment. Math. Helv., 30 (1955), 305-330. | Zbl 0071.16403
[2] , A rational homotopy analog of Whitehead's problem, Proceedings of the 1983 Nordic Conference, Lecture Notes in Math., 1183, Springer Verlag (1983). | Zbl 0591.55005
[3] , Non commutative graded algebras and their Hilbert series, J. Algebra, 78 (1982), 120-140. | MR 84g:16001 | Zbl 0502.16002
[4] , Homotopy exponent for spaces of category two, preprint (1987).
[5] , Hopf algebra up to homotopy, preprint (1988). | Zbl 0681.55006
[6] , Commutator calculus and groups of homotopy classes, London Math. Soc. Lecture Notes series 50, Cambridge University Press (1981). | MR 83b:55012 | Zbl 0473.55001
[7] , On the homotopy classification problem, 5, Homotopy theory of topological mapping cones, Bonn (1984).
[8] et , Minimal models in homotopy theory, Math. Ann. 225-3 (1977), 219-242. | MR 55 #4174 | Zbl 0322.55019
[9] et , Homotopy limits, completions and localisations, Lecture Notes in Math. 304, Springer (1972). | Zbl 0259.55004
[10] , , , et , The radical of the homotopy Lie algebra, Amer. J. Math., 110 (1988), 301-322. | MR 89d:55029 | Zbl 0654.55011
[11] et , Sur l'opération d'holonomie rationnelle. Lecture Notes in Math., 1183, Springer-Verlag (1983), 136-169. | MR 87i:55021 | Zbl 0594.55011
[12] et , The fibre-cofibre construction and its applications, J.P.A.A., 53 (1988), 59-69. | MR 89h:55022 | Zbl 0648.55012
[13] et , Suites inertes dans les algèbres de Lie graduées, Math. Scand., 61 (1987), 39-67. | MR 89e:55022 | Zbl 0655.55004
[14] et , Notions of category in differential algebra, Lecture Notes in Math., 1318, Springer-Verlag (1988), 99-123. | MR 89h:55023 | Zbl 0656.55003
[15] , “Autopsie d'un meurtre” dans une algèbre de chaînes, Ann. Sc. E.N.S., 4-11 (1978), 93-100. | Numdam | Zbl 0382.55011
[16] et , Loop spaces of finite complexes at large primes, Proc. A.M.S., 96-4 (1986), 698-702. | MR 87h:55015 | Zbl 0594.55006
[17] et , On the structure of Hopf algebras, Ann. Math., 821 (1965), 211-264. | MR 30 #4259 | Zbl 0163.28202
[18] , Differential homological algebra, Proc. Int. Cong. Math., I (1970), 1-5. | MR 26 #6229 | Zbl 0337.18009
[19] et , Hopf algebras and multiplicative fibrations, II, Amer. J. Math. | Zbl 0214.50201
[20] , On rationalized H and Co-H spaces with an appendix on decomposable H and Co-H spaces, Manus. Math, 51 (1984), 63-87. | MR 86m:55016 | Zbl 0569.55006
[21] , On adding relations to homotopy groups, Ann. of Math., 2-42 (1941), 409-428. | JFM 67.0738.04 | Zbl 0027.26404
[22] , Elements of homotopy theory, G.T.M., 61, Springer-Verlag (1978). | MR 80b:55001 | Zbl 0406.55001