Spectral gap of scl in free products

TL;DR

This paper establishes a lower bound for stable commutator length in free products of torsion-free groups, extending previous results and providing a new proof of a known theorem.

Contribution

It proves a spectral gap for scl in free products, generalizing Duncan-Howie's theorem with a novel approach.

Findings

scl$_G(g)  1/2$ for certain elements

extends Duncan-Howies theorem

provides a new proof of the spectral gap

Abstract

Let $G=*_\lambda G_\lambda$ be a free product of torsion-free groups, and let $g\in[G,G]$ be any element not conjugate into a $G_\lambda$. Then scl$_G(g)\ge1/2$. This generalizes, and gives a new proof of a theorem of Duncan-Howie.