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Spectral gap of scl in free products


Author: Lvzhou Chen
Journal: Proc. Amer. Math. Soc. 146 (2018), 3143-3151
MSC (2010): Primary 57M07; Secondary 20E06, 20E05, 20F12, 20F65, 20J06
DOI: https://doi.org/10.1090/proc/13899
Published electronically: March 19, 2018
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Abstract | References | Similar Articles | Additional Information

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 $ \textup {scl}_G(g)\ge 1/2$. This generalizes and gives a new proof of a theorem of Duncan and Howie (1991).


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Additional Information

Lvzhou Chen
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
Email: lzchen@math.uchicago.edu

DOI: https://doi.org/10.1090/proc/13899
Received by editor(s): November 28, 2016
Received by editor(s) in revised form: May 19, 2017, and July 19, 2017
Published electronically: March 19, 2018
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society

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