A lower bound on end-periodic stretch factors

TL;DR

This paper establishes a lower bound on the stretch factor of end-periodic homeomorphisms based on their topological complexity, demonstrating the bound's growth rate is optimal.

Contribution

It introduces a new lower bound for the Handel--Miller stretch factor in terms of the core characteristic, a topological complexity measure.

Findings

Lower bound on stretch factor in terms of core characteristic

Growth rate of the bound is proven to be sharp

Provides a quantitative link between topological complexity and stretch factors

Abstract

Given an end-periodic homeomorphism $f: S \to S$ we give a lower bound on the Handel--Miller stretch factor of $f$ in terms of the core characteristic of $f$, which is a measure of topological complexity for an end-periodic homeomorphism. We also show that the growth rate of this bound is sharp.