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Homotopy theory of stratified spaces

Sylvain Douteau

Algebraic & Geometric Topology 21 (2021) 507–541
Abstract

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.

Keywords
stratified homotopy theory, stratified spaces, stratified homotopy groups
Mathematical Subject Classification
Primary: 18N40, 55U35, 57N80
References
Publication
Received: 12 November 2019
Revised: 4 May 2020
Accepted: 25 May 2020
Published: 25 February 2021
Authors
Sylvain Douteau
LAMFA, CNRS UMR 7352
Université de Picardie Jules Verne
Amiens
France