Spectral gap of scl in free products

Abstract

Let $G={\ast }_{\lambda }{G}_{\lambda }$ 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${}_G(g)\ge 1/2$. This generalizes, and gives a new proof of a theorem of Duncan-Howie.

version 2; 9 pages, 4 figures. Revised according to referee's suggestions. To appear in Proceedings of the AMS

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