Algebraic & Geometric Topology Volume 21, issue 1 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Editorial Interests

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author Index

To Appear

Other MSP Journals

Ephemeral persistence modules and distance comparison

Nicolas Berkouk and François Petit

Algebraic & Geometric Topology 21 (2021) 247–277

DOI: 10.2140/agt.2021.21.247

Bibliography

1	T Asano, Y Ike, Persistence-like distance on Tamarkin’s category and symplectic displacement energy, J. Symplectic Geom. 18 (2020) 613 MR4142482
2	P Belmans, A J de Jong, others, The Stacks project, electronic reference (2005–)
3	N Berkouk, Stable resolutions of multi-parameter persistence modules, preprint (2019) arXiv:1901.09824
4	N Berkouk, G Ginot, A derived isometry theorem for constructible sheaves on ℝ, preprint (2018) arXiv:1805.09694
5	F Borceux, Handbook of categorical algebra, I: Basic category theory, 50, Cambridge Univ. Press (1994) MR1291599
6	M B Botnan, W Crawley-Boevey, Decomposition of persistence modules, Proc. Amer. Math. Soc. 148 (2020) 4581 MR4143378
7	G Carlsson, A Zomorodian, The theory of multidimensional persistence, Discrete Comput. Geom. 42 (2009) 71 MR2506738
8	F Chazal, D Cohen-Steiner, M Glisse, L J Guibas, S Y Oudot, Proximity of persistence modules and their diagrams, from: "Proceedings of the 25th annual Symposium on Computational Geometry" (editors J Hershberger, E Fogel), ACM (2009) 237
9	F Chazal, W Crawley-Boevey, V de Silva, The observable structure of persistence modules, Homology Homotopy Appl. 18 (2016) 247 MR3575998
10	F Chazal, V de Silva, M Glisse, S Oudot, The structure and stability of persistence modules, Springer (2016) MR3524869
11	J M Curry, Sheaves, cosheaves and applications, PhD thesis, University of Pennsylvania (2014)
12	P Gabriel, Des catégories abéliennes, Bull. Soc. Math. France 90 (1962) 323 MR232821
13	S Guillermou, P Schapira, Microlocal theory of sheaves and Tamarkin’s non displaceability theorem, from: "Homological mirror symmetry and tropical geometry" (editors R Castano-Bernard, F Catanese, M Kontsevich, T Pantev, Y Soibelman, I Zharkov), Lect. Notes Unione Mat. Ital. 15, Springer (2014) 43 MR3330785
14	M Kashiwara, P Schapira, Sheaves on manifolds, 292, Springer (1990) MR1074006
15	M Kashiwara, P Schapira, Categories and sheaves, 332, Springer (2006) MR2182076
16	M Kashiwara, P Schapira, Persistent homology and microlocal sheaf theory, J. Appl. Comput. Topol. 2 (2018) 83 MR3873181
17	M Kashiwara, P Schapira, Piecewise linear sheaves, Int. Math. Res. Not. (2019)
18	H Krause, Localization theory for triangulated categories, from: "Triangulated categories" (editors T Holm, P Jørgensen, R Rouquier), Lond. Math. Soc. Lect. Note Ser. 375, Cambridge Univ. Press (2010) 161 MR2681709
19	M P Lesnick, Multidimensional interleavings and applications to topological inference, PhD thesis, Stanford University (2012)
20	M Lesnick, The theory of the interleaving distance on multidimensional persistence modules, Found. Comput. Math. 15 (2015) 613 MR3348168
21	M Lesnick, M Wright, Interactive visualization of 2–D persistence modules, preprint (2015) arXiv:1512.00180
22	E Miller, Data structures for real multiparameter persistence modules, preprint (2017) arXiv:1709.08155
23	S Y Oudot, Persistence theory: from quiver representations to data analysis, 209, Amer. Math. Soc. (2015) MR3408277
24	L Polerovich, D Rosen, K Samvelyan, J Zhang, Topological persistence in geometry and analysis, 74, Amer. Math. Soc. (2020)
25	R T Rockafellar, Convex analysis, 28, Princeton Univ. Press (1970) MR0274683
26	V de Silva, E Munch, A Stefanou, Theory of interleavings on categories with a flow, Theory Appl. Categ. 33 (2018) 583 MR3812461