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2018 Scl in free products
Lvzhou Chen
Algebr. Geom. Topol. 18(6): 3279-3313 (2018). DOI: 10.2140/agt.2018.18.3279

Abstract

We study stable commutator length (scl) in free products via surface maps into a wedge of spaces. We prove that scl is piecewise rational linear if it vanishes on each factor of the free product, generalizing a theorem of Danny Calegari. We further prove that the property of isometric embedding with respect to scl is preserved under taking free products. The method of proof gives a way to compute scl in free products which lets us generalize and derive in a new way several well-known formulas. Finally we show independently and in a new approach that scl in free products of cyclic groups behaves in a piecewise quasirational way when the word is fixed but the orders of factors vary, previously proved by Timothy Susse, settling a conjecture of Alden Walker.

Citation

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Lvzhou Chen. "Scl in free products." Algebr. Geom. Topol. 18 (6) 3279 - 3313, 2018. https://doi.org/10.2140/agt.2018.18.3279

Information

Received: 21 July 2017; Revised: 1 May 2018; Accepted: 12 July 2018; Published: 2018
First available in Project Euclid: 27 October 2018

zbMATH: 06990064
MathSciNet: MR3868221
Digital Object Identifier: 10.2140/agt.2018.18.3279

Subjects:
Primary: 57M07
Secondary: 20E06, 20F12, 20F65, 20J06, 52C07

Rights: Copyright © 2018 Mathematical Sciences Publishers

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Vol.18 • No. 6 • 2018
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