Geodesic
Hyperplane restrictions of indecomposable $n$-dimensional persistence modules
Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 291-305.

Voir la notice de l'article provenant de la source International Press of Boston

Understanding the structure of indecomposable $n$‑dimensional persistence modules is a difficult problem, yet is foundational for studying multipersistence. To this end, Buchet and Escolar showed that any finitely presented rectangular $(n-1)$‑dimensional persistence module with finite support is a hyperplane restriction of an indecomposable $n$‑dimensional persistence module. We extend this result to the following: If $M$ is any finitely presented $(n-1)$‑dimensional persistence module with finite support, then there exists an indecomposable ndimensional persistence module $M^\prime$ such that $M$ is the restriction of $M^\prime$ to a hyperplane. We also show that any finite zigzag persistence module is the restriction of some indecomposable $3$‑dimensional persistence module to a path.
DOI : 10.4310/HHA.2022.v24.n2.a14
Classification : 13C05, 55N35
Keywords: persistent homology 
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     author = {Samantha Moore},
     title = {Hyperplane restrictions of indecomposable $n$-dimensional persistence modules},
     journal = {Homology, homotopy, and applications},
     pages = {291--305},
     publisher = {mathdoc},
     volume = {24},
     number = {2},
     year = {2022},
     doi = {10.4310/HHA.2022.v24.n2.a14},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a14/}
}
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Samantha Moore. Hyperplane restrictions of indecomposable $n$-dimensional persistence modules. Homology, homotopy, and applications, Tome 24 (2022) no. 2, pp. 291-305. doi : 10.4310/HHA.2022.v24.n2.a14. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2022.v24.n2.a14/

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