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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 183-213 |
| Number of pages | 31 |
| Journal | Homology, Homotopy and Applications |
| Volume | 23 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 9 Jun 2021 |
| Externally published | Yes |