Quillen-McCord theorem for persistence finite posets

TL;DR

This paper extends the Quillen-McCord theorem to persistence finite posets, providing bounds on the interleaving distance based on fiber contractibility.

Contribution

It introduces a persistence version of the Quillen-McCord theorem, relating homotopy fibers to interleaving distances in persistence finite posets.

Findings

Provides an upper bound for the homotopy interleaving distance between posets.

Establishes a persistence analogue of the classical Quillen-McCord theorem.

Abstract

In this paper, we establish a persistence version of the Quillen-McCord theorem for persistence finite posets. Given a map $f \colon P \rightarrow Q$ between persistence finite posets $P$ and $Q$ with weakly $\varepsilon$-contractible homotopy fibers, we provide an upper bound for the homotopy commutative interleaving distance between $P$ and $Q$.