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2021 Homotopy theory of stratified spaces
Sylvain Douteau
Algebr. Geom. Topol. 21(1): 507-541 (2021). DOI: 10.2140/agt.2021.21.507

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.

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Sylvain Douteau. "Homotopy theory of stratified spaces." Algebr. Geom. Topol. 21 (1) 507 - 541, 2021. https://doi.org/10.2140/agt.2021.21.507

Information

Received: 12 November 2019; Revised: 4 May 2020; Accepted: 25 May 2020; Published: 2021
First available in Project Euclid: 16 March 2021

Digital Object Identifier: 10.2140/agt.2021.21.507

Subjects:
Primary: 18N40 , 55U35 , 57N80

Keywords: stratified homotopy groups , stratified homotopy theory , stratified spaces

Rights: Copyright © 2021 Mathematical Sciences Publishers

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Vol.21 • No. 1 • 2021
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