Homology, Homotopy and Applications

Volume 23 (2021)

Number 2

Invariants for tame parametrised chain complexes

Pages: 183 – 213

DOI: https://dx.doi.org/10.4310/HHA.2021.v23.n2.a11

Authors

Wojciech Chachólski (Department of Mathematics, KTH Stockholm, Sweden)

Barbara Giunti (Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Italy)

Claudia Landi (Dipartimento di Scienze e Metodi dell’Ingegneria, Università di Modena e Reggio Emilia, Italy)

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.

Keywords

topological data analysis, cofibrant approximation, minimality, persistence theory

2010 Mathematics Subject Classification

55Nxx, 55Pxx

The full text of this article is unavailable through your IP address: 35.172.217.174

Received 23 March 2020

Received revised 9 November 2020

Accepted 10 November 2020

Published 9 June 2021