Invariants for tame parametrised chain complexes
Algebraic Topology
2020-11-17 v4
Abstract
We set the foundations for a new approach to Topological Data Analysis (TDA) based on homotopical methods at chain complexes 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.
Cite
@article{arxiv.2003.03969,
title = {Invariants for tame parametrised chain complexes},
author = {Wojciech Chachólski and Barbara Giunti and Claudia Landi},
journal= {arXiv preprint arXiv:2003.03969},
year = {2020}
}