Download this article
 Download this article For screen
For printing
Recent Issues

Volume 26
Issue 7, 2353–2708
Issue 6, 1965–2352
Issue 5, 1597–1963
Issue 4, 1229–1596
Issue 3, 825–1227
Issue 2, 411–824
Issue 1, 1–410

Volume 25, 9 issues

Volume 24, 9 issues

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
 
Author index
To appear
 
Other MSP journals
On stratifications and poset-stratified spaces

Lukas Waas, Jon Woolf and Shoji Yokura

Algebraic & Geometric Topology 26 (2026) 2519–2538
Bibliography
1 P Alexandroff, Diskrete Räume, Mat. Sb. (N.S.) 2 (1937) 501
2 P Alexandrov, Combinatorial topology, Dover (1947)
3 F G Arenas, Alexandroff spaces, Acta Math. Univ. Comenian. (N.S.) 68 (1999) 17 MR1711071
4 J A Barmak, Algebraic topology of finite topological spaces and applications, 2032, Springer (2011) MR3024764
5 C Barwick, S Glasman, P Haine, Exodromy, (2018) arXiv:1807.03281
6 P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
7 R H Bing, Partially continuous decompositions, Proc. Amer. Math. Soc. 6 (1955) 124 MR71003
8 R H Bing, A decomposition of E3 into points and tame arcs such that the decomposition space is topologically different from E3, Ann. of Math. (2) 65 (1957) 484 MR92961
9 R H Bing, The cartesian product of a certain nonmanifold and a line is E4, Ann. of Math. (2) 70 (1959) 399 MR107228
10 J Curry, Sheaves, cosheaves and applications, (2013) arXiv:1303.3255
11 R J Daverman, Decompositions of manifolds, 124, Academic, Orlando, FL (1986) MR872468
12 S Douteau, A simplicial approach to stratified homotopy theory, Trans. Amer. Math. Soc. 374 (2021) 955 MR4196384
13 S Douteau, L Waas, From homotopy links to stratified homotopy theories, (2021) arXiv:2112.02394
14 R Engelking, General topology, 6, Heldermann, Berlin (1989) MR1039321
15 M H Freedman, The topology of four-dimensional manifolds, J. Differential Geometry 17 (1982) 357 MR679066
16 M Freedman, Bing topology and Casson handles, online lectures (2013)
17 M Goresky, R MacPherson, Stratified Morse theory, 14, Springer, Berlin (1988) MR932724
18 P J Haine, On the homotopy theory of stratified spaces, Ann. Sci. Éc. Norm. Supér. (4) 57 (2024) 351 MR4732611
19 B Hughes, Stratified path spaces and fibrations, Proc. Roy. Soc. Edinburgh Sect. A 129 (1999) 351 MR1686706
20 I M James, Alexandroff spaces, Rend. Circ. Mat. Palermo (2) Suppl. 29 (1992) 475 MR1197187
21 J Lurie, Higher algebra, preprint (2017)
22 J N Mather, Stratifications and mappings, from: "Dynamical systems" (editor M M Peixoto), Academic, New York (1973) 195 MR368064
23 J Mather, Notes on topological stability, Bull. Amer. Math. Soc. (N.S.) 49 (2012) 475 MR2958928
24 J P May, Finite topological spaces, notes (2010)
25 R L Moore, Concerning upper semi-continuous collections of continua, Trans. Amer. Math. Soc. 27 (1925) 416 MR1501320
26 R L Moore, Foundations of point set theory, 13, Amer. Math. Soc. (1962) MR150722
27 F Nakaoka, N Oda, Some applications of minimal open sets, Int. J. Math. Math. Sci. 27 (2001) 471 MR1869648
28 S J Nand-Lal, A simplicial approach to stratified homotopy theory, PhD thesis, University of Liverpool (2019) MR4172351
29 n authors, compactly generated topological space, (2026)
30 M Oka, Introduction to mixed hypersurface singularity, from: "Handbook of geometry and topology of singularities II" (editors J L Cisneros-Molina, D T Lê, J Seade), Springer (2021) 403 MR4367442
31 C A M Peters, J H M Steenbrink, Mixed Hodge structures, 52, Springer (2008) MR2393625
32 T Speer, A short study of Alexandroff spaces, (2007) arXiv:0708.2136
33 D Tamaki, Cellular stratified spaces, from: "Combinatorial and toric homotopy" (editors A Darby, J Grbić, Z Lü, J Wu), Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap. 35, World Sci., Hackensack, NJ (2018) 305 MR3792465
34 D Tamaki, H L Tanaka, Stellar stratifications on classifying spaces, from: "Algebraic topology and related topics" (editors M Singh, Y Song, J Wu), Springer (2019) 287 MR3991187
35 R Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969) 240 MR239613
36 L Waas, Combinatorial models for stratified homotopy theory, (2024) arXiv:2403.06280
37 L Waas, On the homotopy links of stratified cell complexes, (2024) arXiv:2403.06272
38 L Waas, Presenting the topological stratified homotopy hypothesis, (2024) arXiv:2403.07686
39 H Whitney, Tangents to an analytic variety, Ann. of Math. (2) 81 (1965) 496 MR192520
40 Wikipedia, Stratified spaces, electronic reference (2025)
41 Wikipedia, Compactly generated space, electronic reference (2026)
42 J Woolf, The fundamental category of a stratified space, J. Homotopy Relat. Struct. 4 (2009) 359 MR2591969
43 J Woolf, Transversal homotopy theory, Theory Appl. Categ. 24 (2010) 148 MR2720181
44 S Yokura, Decomposition spaces and poset-stratified spaces, Tbilisi Math. J. 13 (2020) 101 MR4117809