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Bifiltrations and persistence paths for $2$–Morse functions

Ryan Budney and Tomasz Kaczynski

Algebraic & Geometric Topology 23 (2023) 2895–2924
Bibliography
1 M Allili, T Kaczynski, C Landi, F Masoni, Acyclic partial matchings for multidimensional persistence: algorithm and combinatorial interpretation, J. Math. Imaging Vision 61 (2019) 174 MR3905484
2 M Assif P K, Y Baryshnikov, Biparametric persistence for smooth filtrations, preprint (2021) arXiv:2110.09602
3 A Banyaga, D Hurtubise, Lectures on Morse homology, 29, Kluwer (2004) MR2145196
4 S Biasotti, A Cerri, P Frosini, D Giorgi, C Landi, Multidimensional size functions for shape comparison, J. Math. Imaging Vision 32 (2008) 161 MR2434687
5 R Bott, Lectures on Morse theory, old and new, Bull. Amer. Math. Soc. 7 (1982) 331 MR663786
6 P Bubenik, M J Catanzaro, Multiparameter persistent homology via generalized Morse theory, preprint (2021) arXiv:2107.08856
7 F Cagliari, B Di Fabio, M Ferri, One-dimensional reduction of multidimensional persistent homology, Proc. Amer. Math. Soc. 138 (2010) 3003 MR2644911
8 G Carlsson, A Zomorodian, The theory of multidimensional persistence, Discrete Comput. Geom. 42 (2009) 71 MR2506738
9 N Cavazza, M Ethier, P Frosini, T Kaczynski, C Landi, Comparison of persistent homologies for vector functions: from continuous to discrete and back, Comput. Math. Appl. 66 (2013) 560 MR3079758
10 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
11 A Cerri, M Ethier, P Frosini, On the geometrical properties of the coherent matching distance in 2D persistent homology, J. Appl. Comput. Topol. 3 (2019) 381 MR4025835
12 H Edelsbrunner, J L Harer, Computational topology : An introduction, Amer. Math. Soc. (2010) MR2572029
13 W Fulton, Young tableaux : With applications to representation theory and geometry, 35, Cambridge Univ. Press (1997) MR1464693
14 D T Gay, R Kirby, Indefinite Morse 2–functions : broken fibrations and generalizations, Geom. Topol. 19 (2015) 2465 MR3416108
15 D Gay, R Kirby, Trisecting 4–manifolds, Geom. Topol. 20 (2016) 3097 MR3590351
16 V Guillemin, A Pollack, Differential topology, Prentice-Hall (1974) MR0348781
17 A A Kosinski, Differential manifolds, 138, Academic (1993) MR1190010
18 C Landi, S Scaramuccia, Relative-perfectness of discrete gradient vector fields and multi-parameter persistent homology, J. Comb. Optim. 44 (2022) 2347 MR4496549
19 M Lesnick, Lecture notes for Math 840 : Multiparameter persistence, lecture notes (2019)
20 M Lesnick, M Wright, Interactive visualization of 2–D persistence modules, preprint (2015) arXiv:1512.00180
21 E Miller, Homological algebra of modules over posets, preprint (2020) arXiv:2008.00063
22 J Milnor, Morse theory, 51, Princeton Univ. Press (1963) MR0163331
23 M Mrozek, The Morse equation in Conley’s index theory for homeomorphisms, Topology Appl. 38 (1991) 45 MR1093865
24 J H Rubinstein, S Tillmann, Multisections of piecewise linear manifolds, Indiana Univ. Math. J. 69 (2020) 2209 MR4170091
25 K P Rybakowski, E Zehnder, A Morse equation in Conley’s index theory for semiflows on metric spaces, Ergodic Theory Dynam. Systems 5 (1985) 123 MR782792
26 O Saeki, Topology of singular fibers of differentiable maps, 1854, Springer (2004) MR2106689
27 S Smale, Global analysis and economics : Pareto optimum and a generalization of Morse theory, Synthese 31 (1975) 345 MR470989
28 Y H Wan, Morse theory for two functions, Topology 14 (1975) 217 MR377981
29 H Whitney, On singularities of mappings of euclidean spaces, I : Mappings of the plane into the plane, Ann. of Math. 62 (1955) 374 MR73980