June 2023 Lipschitz metric isometries between outer spaces of virtually free groups
Rylee Alanza Lyman
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Illinois J. Math. 67(2): 409-422 (June 2023). DOI: 10.1215/00192082-10592435


Dowdall and Taylor observed that, given a finite-index subgroup of a free group, taking covers induces an embedding from the outer space of the free group to the outer space of the subgroup, this embedding is an isometry with respect to the (asymmetric) Lipschitz metric and that the embedding sends folding paths to folding paths. The purpose of this note is to extend this result to virtually free groups. We further extend a result of Francaviglia and Martino, proving the existence of “candidates” for the Lipschitz distance between points in the outer space of the virtually free group. Additionally, we identify a deformation retraction of the spine of the outer space for the virtually free group with the space considered by Krstić and Vogtmann.


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Rylee Alanza Lyman. "Lipschitz metric isometries between outer spaces of virtually free groups." Illinois J. Math. 67 (2) 409 - 422, June 2023. https://doi.org/10.1215/00192082-10592435


Received: 12 September 2022; Revised: 25 January 2023; Published: June 2023
First available in Project Euclid: 20 February 2023

MathSciNet: MR4593897
zbMATH: 07724278
Digital Object Identifier: 10.1215/00192082-10592435

Primary: 20E08
Secondary: 20F65

Rights: Copyright © 2023 by the University of Illinois at Urbana–Champaign


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Vol.67 • No. 2 • June 2023
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