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On stratifications and
poset-stratified spaces
Lukas Waas, Jon Woolf and Shoji Yokura |
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Algebraic & Geometric Topology 26 (2026) 2519–2538
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Abstract |
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A stratified space is a topological space equipped with a stratification, which is a decomposition or partition of the topological space satisfying certain extra conditions. More recently, the notion of poset-stratified space, i.e., topological space endowed with a continuous map to a poset with its Alexandrov topology, has been popularized. Both notions of stratified spaces are ubiquitous in mathematics, ranging from investigations of singular structures in algebraic geometry to extensions of the homotopy hypothesis in higher category theory. In this article we study the precise mathematical relation between these different approaches to stratified spaces. |
Keywords
stratification, poset-stratified space, decomposition
space, poset, Alexandrov topology
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Mathematical Subject Classification
Primary: 32S60, 54B15, 57N80
Secondary: 06A99
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References |
Publication
Received: 26 July 2024
Revised: 22 March 2025
Accepted: 2 July 2025
Published: 1 September 2026
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Authors |
| Lukas Waas | |
| Department of Mathematics Oxford University Oxford United Kingdom |
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| Jon Woolf | |
| Department of Mathematical
Sciences University of Liverpool Liverpool United Kingdom |
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| Shoji Yokura | |
| Graduate School of Science and
Engineering Kagoshima University Kagoshima Japan |
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| © 2026 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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