Algebraic & Geometric Topology Volume 19, issue 2 (2019)

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

Parametrized homology via zigzag persistence

Gunnar Carlsson, Vin de Silva, Sara Kališnik and Dmitriy Morozov

Algebraic & Geometric Topology 19 (2019) 657–700

DOI: 10.2140/agt.2019.19.657

Bibliography

1	H Adams, G Carlsson, Evasion paths in mobile sensor networks, Internat. J. Robotics Res. 34 (2015) 90
2	P K Agarwal, H Edelsbrunner, J Harer, Y Wang, Extreme elevation on a 2–manifold, Discrete Comput. Geom. 36 (2006) 553 MR2267546
3	M Auslander, Representation theory of Artin algebras, II, Comm. Algebra 1 (1974) 269 MR0349747
4	G Azumaya, Corrections and supplementaries to my paper concerning Krull–Remak–Schmidt’s theorem, Nagoya Math. J. 1 (1950) 117 MR0037832
5	S Basu, R Pollack, M F Roy, Algorithms in real algebraic geometry, 10, Springer (2006) MR2248869
6	U Bauer, M Lesnick, Induced matchings of barcodes and the algebraic stability of persistence, from: "Computational geometry" (editors S W Cheng, O Devillers), ACM (2014) 355 MR3382316
7	P Bendich, H Edelsbrunner, D Morozov, A Patel, Homology and robustness of level and interlevel sets, Homology Homotopy Appl. 15 (2013) 51 MR3031814
8	I N Bernšteĭn, I M Gel’fand, V A Ponomarev, Coxeter functors, and Gabriel’s theorem, Uspehi Mat. Nauk 28 (1973) 19 MR0393065
9	D Burghelea, A refinement of Betti numbers and homology in the presence of a continuous function, I, Algebr. Geom. Topol. 17 (2017) 2051 MR3685602
10	D Burghelea, T K Dey, Topological persistence for circle-valued maps, Discrete Comput. Geom. 50 (2013) 69 MR3070542
11	D Burghelea, S Haller, Topology of angle valued maps, bar codes and Jordan blocks, J. Appl. Comput. Topol. 1 (2017) 121
12	F Cagliari, C Landi, Finiteness of rank invariants of multidimensional persistent homology groups, Appl. Math. Lett. 24 (2011) 516 MR2749737
13	G Carlsson, V de Silva, Zigzag persistence, Found. Comput. Math. 10 (2010) 367 MR2657946
14	G Carlsson, V de Silva, D Morozov, Zigzag persistent homology and real-valued functions, from: "Proceedings of the 25th annual Symposium on Computational Geometry" (editors J Hershberger, E Fogel), ACM (2009) 247
15	A Cerri, B Di Fabio, M Ferri, P Frosini, C Landi, Betti numbers in multidimensional persistent homology are stable functions, Math. Methods Appl. Sci. 36 (2013) 1543 MR3083259
16	F Chazal, D Cohen-Steiner, M Glisse, L Guibas, S 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
17	F Chazal, V de Silva, M Glisse, S Oudot, The structure and stability of persistence modules, Springer (2016) MR3524869
18	D Cohen-Steiner, H Edelsbrunner, J Harer, Stability of persistence diagrams, Discrete Comput. Geom. 37 (2007) 103 MR2279866
19	D Cohen-Steiner, H Edelsbrunner, J Harer, Extending persistence using Poincaré and Lefschetz duality, Found. Comput. Math. 9 (2009) 79 MR2472288
20	W Crawley-Boevey, Decomposition of pointwise finite-dimensional persistence modules, J. Algebra Appl. 14 (2015) MR3323327
21	T K Dey, R Wenger, Stability of critical points with interval persistence, Discrete Comput. Geom. 38 (2007) 479 MR2352705
22	L van den Dries, Tame topology and o–minimal structures, 248, Cambridge Univ. Press (1998) MR1633348
23	H Edelsbrunner, D Letscher, A Zomorodian, Topological persistence and simplification, Discrete Comput. Geom. 28 (2002) 511 MR1949898
24	H Edelsbrunner, D Morozov, A Patel, The stability of the apparent contour of an orientable 2–manifold, from: "Topological methods in data analysis and visualization" (editors V Pascucci, X Tricoche, H Hagen, J Tierny), Springer (2011) 27 MR2798444
25	S Eilenberg, N Steenrod, Foundations of algebraic topology, Princeton Univ. Press (1952) MR0050886
26	S C Ferry, Remarks on Steenrod homology, from: "Novikov conjectures, index theorems and rigidity, II" (editors S C Ferry, A Ranicki, J Rosenberg), London Math. Soc. Lecture Note Ser. 227, Cambridge Univ. Press (1995) 148 MR1388310
27	P Gabriel, Unzerlegbare Darstellungen, I, Manuscripta Math. 6 (1972) 71 MR0332887
28	S Kališnik, Alexander duality for parametrized homology, Homology Homotopy Appl. 15 (2013) 227 MR3138378
29	S Kališnik, Persistent homology and duality, PhD thesis, University of Ljubljana (2013)
30	J Milnor, On the Steenrod homology theory, mimeographed notes (1960)
31	V de Silva, E Munch, A Patel, Categorified Reeb graphs, Discrete Comput. Geom. 55 (2016) 854 MR3505333
32	J E West, Mapping Hilbert cube manifolds to ANR’s : a solution of a conjecture of Borsuk, Ann. of Math. 106 (1977) 1 MR0451247
33	A Zomorodian, G Carlsson, Computing persistent homology, Discrete Comput. Geom. 33 (2005) 249 MR2121296