Persistent homotopy theory
Algebraic Topology
2020-10-28 v3
Abstract
Vietoris-Rips and degree Rips complexes are represented as homotopy types by their underlying posets of simplices, and basic homotopy stability theorems are recast in these terms. These homotopy types are viewed as systems (or functors), which are defined on a parameter space. The category of systems of spaces admits a partial homotopy theory that is based on controlled equivalences, suitably defined, that are the output of homotopy stability results.
Cite
@article{arxiv.2002.10013,
title = {Persistent homotopy theory},
author = {J. F. Jardine},
journal= {arXiv preprint arXiv:2002.10013},
year = {2020}
}
Comments
21 pages. This is a new version of this preprint. The proof of Lemma 19 of the previous version had an error that rendered the proof of the former Theorem 23 invalid. No statement of that form is now claimed