Rectification of interleavings and a persistent Whitehead theorem

Lanari, Edoardo; Scoccola, Luis

doi:10.2140/agt.2023.23.803

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Rectification of interleavings and a persistent Whitehead theorem

Edoardo Lanari and Luis Scoccola

Algebraic & Geometric Topology 23 (2023) 803–832

DOI: 10.2140/agt.2023.23.803

Abstract

The homotopy interleaving distance, a distance between persistent spaces, was introduced by Blumberg and Lesnick and shown to be universal, in the sense that it is the largest homotopy-invariant distance for which sublevel-set filtrations of close-by real-valued functions are close-by. There are other ways of constructing homotopy-invariant distances, but not much is known about the relationships between these choices. We show that other natural distances differ from the homotopy interleaving distance in at most a multiplicative constant, and prove versions of the persistent Whitehead theorem, a conjecture of Blumberg and Lesnick that relates morphisms that induce interleavings in persistent homotopy groups to stronger homotopy-invariant notions of interleaving.

Keywords

homotopy interleaving, rectification, Whitehead theorem

Mathematical Subject Classification

Primary: 55N31, 62R40

Secondary: 18N40, 18N50, 55U10, 55U35

References

Publication

Received: 8 February 2021

Revised: 6 July 2021

Accepted: 30 October 2021

Published: 9 May 2023

Authors

Edoardo Lanari
Institute of Mathematics Czech Academy of Sciences Prague Czech Republic
http://edolana.github.io
Luis Scoccola
Department of Mathematics Northeastern University Boston, MA United States
http://luisscoccola.github.io

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Volume 23, issue 2 (2023)