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}, pages = {33--47}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {35}, number = {3}, year = {1985}, doi = {10.5802/aif.1017}, mrnumber = {87e:55008}, zbl = {0563.55005}, language = {fr}, url = {http://www.numdam.org/articles/10.5802/aif.1017/} }
TY - JOUR AU - Didierjean, Geneviève TI - Homotopie de l'espace des équivalences d'homotopie fibrées JO - Annales de l'Institut Fourier PY - 1985 SP - 33 EP - 47 VL - 35 IS - 3 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1017/ DO - 10.5802/aif.1017 LA - fr ID - AIF_1985__35_3_33_0 ER -
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/articles/10.5802/aif.1017/
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