Consider a push-out diagram of spaces , construct the homotopy push-out, and then the homotopy pull-back of the diagram one gets by forgetting the initial object . We compare the difference between and this homotopy pull-back. This difference is measured in terms of the homotopy fibers of the original maps. Restricting our attention to the connectivity of these maps, we recover the classical Blakers–Massey Theorem.
Considérons un diagramme d’espaces , construisons le push-out homotopique, puis le pull-back homotopique du diagramme obtenu en oubliant l’objet initial . Nous comparons la différence entre et ce pull-back homomotopique. Cette différence est mesurée en termes des fibres homotopiques des applications originales. En restreignant notre attention sur la connectivité de ces applications nous obtenons la version classique du Théorème de Blakers–Massey.
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Keywords: homotopy excision, cellular inequality, total fiber, homotopy localization
Mot clés : excision homotopique, inégalité cellulaire, fibre totale, localisation homotopique
@article{AIF_2016__66_6_2641_0,
author = {Chach\'olski, Wojciech and Scherer, J\'er\^ome and Werndli, Kay},
title = {Homotopy excision and cellularity},
journal = {Annales de l'Institut Fourier},
pages = {2641--2665},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {66},
number = {6},
year = {2016},
doi = {10.5802/aif.3074},
language = {en},
url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3074/}
}
TY - JOUR AU - Chachólski, Wojciech AU - Scherer, Jérôme AU - Werndli, Kay TI - Homotopy excision and cellularity JO - Annales de l'Institut Fourier PY - 2016 SP - 2641 EP - 2665 VL - 66 IS - 6 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3074/ DO - 10.5802/aif.3074 LA - en ID - AIF_2016__66_6_2641_0 ER -
%0 Journal Article %A Chachólski, Wojciech %A Scherer, Jérôme %A Werndli, Kay %T Homotopy excision and cellularity %J Annales de l'Institut Fourier %D 2016 %P 2641-2665 %V 66 %N 6 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3074/ %R 10.5802/aif.3074 %G en %F AIF_2016__66_6_2641_0
Chachólski, Wojciech; Scherer, Jérôme; Werndli, Kay. Homotopy excision and cellularity. Annales de l'Institut Fourier, Volume 66 (2016) no. 6, pp. 2641-2665. doi : 10.5802/aif.3074. https://aif.centre-mersenne.org/articles/10.5802/aif.3074/
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