Algebraic & Geometric Topology Volume 21, issue 3 (2021)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Other MSP Journals

Barcode embeddings for metric graphs

Steve Oudot and Elchanan Solomon

Algebraic & Geometric Topology 21 (2021) 1209–1266

DOI: 10.2140/agt.2021.21.1209

Bibliography

1	U Bauer, X Ge, Y Wang, Measuring distance between Reeb graphs, from: "Proceedings of the 30th annual Symposium on Computational Geometry" (editors S W Cheng, O Devillers, K Buchin), ACM (2014) 464 MR3382328
2	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
3	D Burago, Y Burago, S Ivanov, A course in metric geometry, 33, Amer. Math. Soc. (2001) MR1835418
4	M Carrière, S Oudot, Local equivalence and intrinsic metrics between Reeb graphs, from: "33rd International Symposium on Computational Geometry" (editors B Aronov, M J Katz), Leibniz Int. Proc. Informatics 77, Schloss Dagstuhl. Leibniz-Zent. Inform. (2017) MR3685697
5	F Chazal, V de Silva, M Glisse, S Oudot, The structure and stability of persistence modules, Springer (2016) MR3524869
6	F Chazal, V de Silva, S Oudot, Persistence stability for geometric complexes, Geom. Dedicata 173 (2014) 193 MR3275299
7	D Cohen-Steiner, H Edelsbrunner, J Harer, Extending persistence using Poincaré and Lefschetz duality, Found. Comput. Math. 9 (2009) 79 MR2472288
8	J Curry, The fiber of the persistence map for functions on the interval, J. Appl. Comput. Topol. 2 (2018) 301 MR3927355
9	T K Dey, D Shi, Y Wang, Comparing graphs via persistence distortion, from: "31st International Symposium on Computational Geometry" (editor L Arge), Leibniz Int. Proc. Informatics 34, Schloss Dagstuhl. Leibniz-Zent. Inform. (2015) 491 MR3392801
10	M Gameiro, Y Hiraoka, I Obayashi, Continuation of point clouds via persistence diagrams, Phys. D 334 (2016) 118 MR3545973
11	E Gasparovic, M Gommel, E Purvine, R Sazdanovic, B Wang, Y Wang, L Ziegelmeier, A complete characterization of the one-dimensional intrinsic Čech persistence diagrams for metric graphs, from: "Research in computational topology" (editors E W Chambers, B T Fasy, L Ziegelmeier), Assoc. Women Math. Ser. 13, Springer (2018) 33 MR3905000
12	A Ivanov, S Iliadis, A Tuzhilin, Realizations of Gromov–Hausdorff distance, preprint (2016) arXiv:1603.08850
13	M Kerber, D Morozov, A Nigmetov, Geometry helps to compare persistence diagrams, ACM J. Exp. Algorithmics 22 (2017) MR3707737
14	F Mémoli, Gromov–Wasserstein distances and the metric approach to object matching, Found. Comput. Math. 11 (2011) 417 MR2811584
15	K Turner, S Mukherjee, D M Boyer, Persistent homology transform for modeling shapes and surfaces, Inf. Inference 3 (2014) 310 MR3311455