Abstract
Given a free factor of the rank free group , we characterize when the subgroup of that stabilizes the conjugacy class of is distorted in . We also prove that the image of the natural embedding of in is nondistorted, that the stabilizer in of the conjugacy class of any free splitting of is nondistorted and we characterize when the stabilizer of the conjugacy class of an arbitrary free factor system of is distorted. In all proofs of nondistortion, we prove the stronger statement that the subgroup in question is a Lipschitz retract. As applications we determine Dehn functions and automaticity for and .
Citation
Michael Handel. Lee Mosher. "Lipschitz retraction and distortion for subgroups of $\mathsf{Out}(F_n)$." Geom. Topol. 17 (3) 1535 - 1579, 2013. https://doi.org/10.2140/gt.2013.17.1535
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