Volume 21, issue 1 (2021)

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

Volume 25, 1 issue

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
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
Homotopy theory of stratified spaces

Sylvain Douteau

Algebraic & Geometric Topology 21 (2021) 507–541
Bibliography
1 M Banagl, Rational generalized intersection homology theories, Homology Homotopy Appl. 12 (2010) 157 MR2607414
2 C Barwick, S Glasman, P Haine, Exodromy, preprint (2018) arXiv:1807.03281
3 A Borel, A Haefliger, N Habegger, M Goresky, R MacPherson, N A’Campo, P P Grivel, Intersection cohomology, 50, Birkhäuser (1984) MR788171
4 P Cagne, P A Melliès, On bifibrations of model categories, Adv. Math. 370 (2020) MR4099827
5 D Chataur, M Saralegi-Aranguren, D Tanré, Intersection cohomology, simplicial blow-up and rational homotopy, 1214, Amer. Math. Soc. (2018) MR3796432
6 S Douteau, A simplicial approach to stratified homotopy theory, preprint (2018) arXiv:1801.04797
7 D Dugger, Notes on delta-generated spaces, preprint (2003)
8 G Friedman, Singular intersection theory, preprint (2019)
9 G Friedman, J E McClure, Cup and cap products in intersection (co)homology, Adv. Math. 240 (2013) 383 MR3046315
10 M Goresky, R MacPherson, Intersection homology theory, Topology 19 (1980) 135 MR572580
11 M Goresky, R MacPherson, Intersection homology, II, Invent. Math. 72 (1983) 77 MR696691
12 P J Haine, On the homotopy theory of stratified spaces, preprint (2018) arXiv:1811.01119
13 A Henriques, A model category for stratified spaces, preprint (2014)
14 K Hess, M Kędziorek, E Riehl, B Shipley, A necessary and sufficient condition for induced model structures, J. Topol. 10 (2017) 324 MR3653314
15 P S Hirschhorn, Model categories and their localizations, 99, Amer. Math. Soc. (2003) MR1944041
16 H C King, Topological invariance of intersection homology without sheaves, Topology Appl. 20 (1985) 149 MR800845
17 J Lurie, Higher algebra, preprint (2017)
18 D A Miller, Strongly stratified homotopy theory, Trans. Amer. Math. Soc. 365 (2013) 4933 MR3066775
19 J Milnor, The geometric realization of a semi-simplicial complex, Ann. of Math. 65 (1957) 357 MR84138
20 S J Nand-Lal, A simplicial approach to stratified homotopy theory, PhD thesis, University of Liverpool (2019)
21 F Quinn, Homotopically stratified sets, J. Amer. Math. Soc. 1 (1988) 441 MR928266
22 D Tamaki, H L Tanaka, Stellar stratifications on classifying spaces, from: "Algebraic topology and related topics" (editors M Singh, Y Song, J Wu), Birkhäuser (2019) 287 MR3991187
23 R Thom, Ensembles et morphismes stratifiés, Bull. Amer. Math. Soc. 75 (1969) 240 MR239613
24 D Treumann, Exit paths and constructible stacks, Compos. Math. 145 (2009) 1504 MR2575092
25 H Whitney, Tangents to an analytic variety, Ann. of Math. 81 (1965) 496 MR192520
26 J Woolf, The fundamental category of a stratified space, J. Homotopy Relat. Struct. 4 (2009) 359 MR2591969