Geodesic
Invariants for tame parametrised chain complexes
Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 183-213.

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

We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at the chain complex level. We present the category of tame parametrised chain complexes as a comprehensive environment that includes several cases that usually TDA handles separately, such as persistence modules, zigzag modules, and commutative ladders. We extract new invariants in this category using a model structure and various minimal cofibrant approximations. Such approximations and their invariants retain some of the topological, and not just homological, aspects of the objects they approximate.
DOI : 10.4310/HHA.2021.v23.n2.a11
Classification : 55Nxx, 55Pxx
Keywords: topological data analysis, cofibrant approximation, minimality, persistence theory 
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Wojciech Chachólski; Barbara Giunti; Claudia Landi. Invariants for tame parametrised chain complexes. Homology, homotopy, and applications, Tome 23 (2021) no. 2, pp. 183-213. doi : 10.4310/HHA.2021.v23.n2.a11. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2021.v23.n2.a11/

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