A curvature-free Log(2k-1) Theorem

TL;DR

This paper introduces a curvature-free version of the Log(2k-1) Theorem, extending previous results and providing a new dimension-independent Collar Lemma, with a straightforward proof leveraging existing work on volume entropy.

Contribution

It generalizes the Log(2k-1) Theorem without curvature assumptions and derives a curvature-free Collar Lemma in all dimensions, simplifying the proof process.

Findings

Curvature-free Log(2k-1) Theorem established

Dimension-independent Collar Lemma derived

Simplified proof leveraging volume entropy results

Abstract

This paper presents a curvature-free version of the Log(2k-1) Theorem of Anderson, Canary, Culler & Shalen [ACCS96]. It generalizes a result by Hou [Hou01] and its proof is rather straightforward once we know the work by Lim [Lim08] on volume entropy for graphs. As a byproduct we obtain a curvature-free version of the Collar Lemma in all dimensions.