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arXiv · 2307.13502

Growth and displacement of free product automorphisms

Matthew Collins
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Abstract

It is well known for an irreducible free group automorphism that its growth rate is equal to the minimal Lipschitz displacement of its action on Culler-Vogtmann space. This follows as a consequence of the existence of train track representatives for the automorphism. We extend this result to the general - possibly reducible - case as well as to the free product situation where growth is replaced by `relative growth'.

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Matthew Collins. 2023-07-25. Growth and displacement of free product automorphisms. https://arxiv.org/abs/2307.13502

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