Homotopy excision and cellularity
Annales de l'Institut Fourier, Volume 66 (2016) no. 6, p. 2641-2665

Consider a push-out diagram of spaces CAB, construct the homotopy push-out, and then the homotopy pull-back of the diagram one gets by forgetting the initial object A. We compare the difference between A 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 CAB, construisons le push-out homotopique, puis le pull-back homotopique du diagramme obtenu en oubliant l’objet initial A. Nous comparons la différence entre A 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.

Received : 2015-09-28
Revised : 2015-12-21
Accepted : 2016-03-24
Published online : 2016-10-04
DOI : https://doi.org/10.5802/aif.3074
Classification:  55P65,  55U35,  55P35,  55P40,  18A30
Keywords: homotopy excision, cellular inequality, total fiber, homotopy localization
@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},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {6},
     year = {2016},
     pages = {2641-2665},
     doi = {10.5802/aif.3074},
     language = {en},
     url = {http://www.numdam.org/item/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. http://www.numdam.org/item/AIF_2016__66_6_2641_0/

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