Persistent homotopy theory

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.

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

Cited by in corpus (3)

• Rectification of interleavings and a persistent Whitehead theorem
• Persistent Homotopy Groups of Metric Spaces
• Branch points and stability