English

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

Geometric Topology 2023-04-03 v3 Differential Geometry Metric Geometry

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.

Cite

@article{arxiv.1909.06124,
  title  = {A curvature-free Log(2k-1) Theorem},
  author = {Florent Balacheff and Louis Merlin},
  journal= {arXiv preprint arXiv:1909.06124},
  year   = {2023}
}

Comments

Accepted for publication in Proceedings of the AMS. Title Changed (formerly entitled "Volume entropy and lengths of homotopically independent loops")

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