Algebraic & Geometric Topology Volume 24, issue 8 (2024)

Download this article
	For screen
	For printing

Recent 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

Interleaving Mayer–Vietoris spectral sequences

Álvaro Torras-Casas and Ulrich Pennig

Algebraic & Geometric Topology 24 (2024) 4265–4306

DOI: 10.2140/agt.2024.24.4265

Bibliography

1	U Bauer, Persistence in discrete Morse theory, PhD thesis, Universität Göttingen (2011)
2	A Björner, Nerves, fibers and homotopy groups, J. Combin. Theory Ser. A 102 (2003) 88 MR1970978
3	N J Cavanna, Methods in homology inference, doctoral dissertations, University of Connecticut (2019)
4	N J Cavanna, K P Gardner, D R Sheehy, When and why the topological coverage criterion works, from: "Proceedings of the Twenty-Eighth Annual ACM–SIAM Symposium on Discrete Algorithms" (editor P N Klein), SIAM (2017) 2679 MR3627906
5	F Chazal, S Y Oudot, Towards persistence-based reconstruction in Euclidean spaces, from: "Computational geometry", ACM (2008) 232 MR2504289
6	É Colin de Verdière, G Ginot, X Goaoc, Helly numbers of acyclic families, Adv. Math. 253 (2014) 163 MR3148550
7	G E Cooke, R L Finney, Homology of cell complexes, Princeton Univ. Press (1967) MR0219059
8	D Dugger, A primer on homotopy colimits, book project (2008)
9	J Ebert, O Randal-Williams, Semisimplicial spaces, Algebr. Geom. Topol. 19 (2019) 2099 MR3995026
10	S Eilenberg, S MacLane, Acyclic models, Amer. J. Math. 75 (1953) 189 MR0052766
11	G Ellis, An invitation to computational homotopy, Oxford Univ. Press (2019) MR3971587
12	D Govc, P Skraba, An approximate nerve theorem, Found. Comput. Math. 18 (2018) 1245 MR3857910
13	A Hatcher, Algebraic topology, Cambridge Univ. Press (2002)
14	T Kaczynski, K Mischaikow, M Mrozek, Computational homology, 157, Springer (2004) MR2028588
15	D Kozlov, Combinatorial algebraic topology, 21, Springer (2008) MR2361455
16	R Lewis, D Morozov, Parallel computation of persistent homology using the blowup complex, from: "Proceedings of the 27th ACM Symposium on Parallelism in Algorithms and Architectures", ACM (2015) 323
17	W S Massey, A basic course in algebraic topology, 127, Springer (1991) MR1095046
18	J P May, A concise course in algebraic topology, Univ. Chicago Press (1999) MR1702278
19	J McCleary, A user’s guide to spectral sequences, 58, Cambridge Univ. Press (2001) MR1793722
20	J R Munkres, Elements of algebraic topology, Addison-Wesley (1984) MR0755006
21	V Nanda, Discrete Morse theory for filtrations, PhD thesis, Rutgers, The State University of New Jersey (2012) MR3152455
22	S Y Oudot, Persistence theory: from quiver representations to data analysis, 209, Amer. Math. Soc. (2015) MR3408277
23	M Robinson, Assignments to sheaves of pseudometric spaces, Compositionality 2 (2020) 25 MR4286925
24	J P Serre, Faisceaux algébriques cohérents, Ann. of Math. 61 (1955) 197 MR0068874
25	E Sköldberg, Morse theory from an algebraic viewpoint, Trans. Amer. Math. Soc. 358 (2006) 115 MR2171225
26	Á Torras-Casas, Distributing persistent homology via spectral sequences, Discrete Comput. Geom. 70 (2023) 580 MR4650017
27	I H R Yoon, R Ghrist, Persistence by parts: multiscale feature detection via distributed persistent homology, preprint (2020) arXiv:2001.01623
28	A Zomorodian, G Carlsson, Localized homology, Comput. Geom. 41 (2008) 126 MR2442490