Homotopie de l'espace des équivalences d'homotopie fibrées
Annales de l'Institut Fourier, Volume 35 (1985) no. 3, p. 33-47

We construct a spectral sequence converging to the bigraded group associated with a suitable filtration of the homotopy groups of the simplicial monoid consisting of the fibre homotopy equivalences from a Kan fibration into itself. In particular, we calculate the homotopy group of self-equivalences of spaces with three non vanishing homotopy groups under their dimension.

On construit une suite spectrale qui converge vers le bigradué associé à une filtration convenable des groupes d’homotopie du monoïde simplicial des équivalences d’homotopie fibrées d’un fibré de Kan dans lui-même. On obtient de nouveaux calculs de ces groupes. En particulier, on calcule le groupe des classes d’homotopie des équivalences d’homotopie d’un espace ayant trois groupes d’homotopie non nuls en dessous de sa dimension.

@article{AIF_1985__35_3_33_0,
     author = {Didierjean, Genevi\`eve},
     title = {Homotopie de l'espace des \'equivalences d'homotopie fibr\'ees},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {35},
     number = {3},
     year = {1985},
     pages = {33-47},
     doi = {10.5802/aif.1017},
     zbl = {0563.55005},
     mrnumber = {87e:55008},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1985__35_3_33_0}
}
Didierjean, Geneviève. Homotopie de l'espace des équivalences d'homotopie fibrées. Annales de l'Institut Fourier, Volume 35 (1985) no. 3, pp. 33-47. doi : 10.5802/aif.1017. http://www.numdam.org/item/AIF_1985__35_3_33_0/

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