Geodesic
Bifiltrations and persistence paths for 2–Morse functions
Budney, Ryan1 ; Kaczynski, Tomasz2
1 Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
2 Département de Mathématiques, Université de Sherbrooke, Sherbrooke, QC, Canada
Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2895-2924

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We study the homotopy type of bifiltrations of compact manifolds induced as the preimage of filtrations of ℝ2 for generic smooth functions f : M → ℝ2. The primary goal of the paper is to allow for a simple description of the multigraded persistent homology associated to such filtrations. Our main result is a description of the evolution of the bifiltration of f in terms of cellular attachments. Analogs of the Morse–Conley equation and Morse inequalities along so-called persistence paths are derived, and a scheme for computing pathwise barcodes is proposed.

DOI : 10.2140/agt.2023.23.2895
Keywords: persistent homology, Morse theory, bifiltrations

Budney, Ryan 1 ; Kaczynski, Tomasz 2

1 Mathematics and Statistics, University of Victoria, Victoria, BC, Canada
2 Département de Mathématiques, Université de Sherbrooke, Sherbrooke, QC, Canada 
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Budney, Ryan; Kaczynski, Tomasz. Bifiltrations and persistence paths for 2–Morse functions. Algebraic and Geometric Topology, Tome 23 (2023) no. 6, pp. 2895-2924. doi: 10.2140/agt.2023.23.2895

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