Homotopy excision and cellularity

Chachólski, Wojciech; Scherer, Jérôme; Werndli, Kay

Annales de l'Institut Fourier, Tome 66 (2016) no. 6, pp. 2641-2665.

Considérons un diagramme d’espaces $C\leftarrow A\to B$, 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.

Consider a push-out diagram of spaces $C\leftarrow A\to B$, 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.

Classification : 55P65, 55U35, 55P35, 55P40, 18A30
Keywords: homotopy excision, cellular inequality, total fiber, homotopy localization
Mot clés : excision homotopique, inégalité cellulaire, fibre totale, localisation homotopique

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