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The Sharp Commutator Bound for the Polymath14 Inequality

Primarily human-written textHuman understanding: all partsmath.GR — Group Theorymath.GT — Geometric Topology

Contributed by Jaeyeon Shim ↗

Version 1 / Oct 09, 2026 / CC BY 4.0

Abstract

We present a simplified proof of the Polymath14 inequality, along with a new sharpness result.

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References

  1. D.H.J. Polymath, Homogeneous length functions on groups , Algebra Number Theory 12 (2018), 1773--1786; https://arxiv.org/abs/1801.03908 arXiv:1801.03908 .arXiv
  2. M. Culler, Using surfaces to solve equations in free groups , Topology 20 (1981), 133--145.
  3. D. Calegari, scl , MSJ Memoirs, vol. 20, Mathematical Society of Japan, Tokyo, 2009.

Version history

  1. v1Submitted by Jaeyeon ShimRevised after moderator-requested changesCurrentOct 09, 2026