Spectral gap of scl in free products

Abstract

Let G = ∗ λ G λ G=*_\lambda G_\lambda be a free product of torsion-free groups, and let g ∈ [ G , G ] g\in [G,G] be any element not conjugate into a G λ G_\lambda . Then s c l G ( g ) ≥ 1 / 2 \mathrm {scl}_G(g)\ge 1/2 . This generalizes and gives a new proof of a theorem of Duncan and Howie (1991).