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.

Invariants for tame parametrised chain complexes / Chachólski, Wojciech; Giunti, Barbara; Landi, Claudia. - In: HOMOLOGY, HOMOTOPY AND APPLICATIONS. - ISSN 1532-0073. - 23:2(2021), pp. 183-213. [10.4310/HHA.2021.v23.n2.a11]

Invariants for tame parametrised chain complexes

Giunti, Barbara;Landi, Claudia
2021

Abstract

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.
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Invariants for tame parametrised chain complexes / Chachólski, Wojciech; Giunti, Barbara; Landi, Claudia. - In: HOMOLOGY, HOMOTOPY AND APPLICATIONS. - ISSN 1532-0073. - 23:2(2021), pp. 183-213. [10.4310/HHA.2021.v23.n2.a11]
Chachólski, Wojciech; Giunti, Barbara; Landi, Claudia
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1246423
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