Volume 21, issue 1 (2021)

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Homotopy theory of stratified spaces

Sylvain Douteau

Algebraic & Geometric Topology 21 (2021) 507–541

We construct a cofibrantly generated model structure on the category of spaces stratified over a fixed poset, and show that it is Quillen-equivalent to a category of diagrams of simplicial sets. Then, considering all those model structures together, we construct a cofibrantly generated model structure on the category of all stratified spaces. In both model categories, weak equivalences are characterized by stratified homotopy groups.

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stratified homotopy theory, stratified spaces, stratified homotopy groups
Mathematical Subject Classification
Primary: 18N40, 55U35, 57N80
Received: 12 November 2019
Revised: 4 May 2020
Accepted: 25 May 2020
Published: 25 February 2021
Sylvain Douteau
Université de Picardie Jules Verne