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arXiv · 2207.12518

The Automorphism Group of the Infinite-Rank Free Group is Coarsely Bounded

George Domat·Hannah Hoganson·Sanghoon Kwak
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Abstract

We prove that the full automorphism group and the outer automorphism group of the free group of countably infinite rank are coarsely bounded. That is, these groups admit no continuous actions on a metric space with unbounded orbits, and have the quasi-isometry type of a point.

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George Domat, Hannah Hoganson, Sanghoon Kwak. 2022-07-25. The Automorphism Group of the Infinite-Rank Free Group is Coarsely Bounded. https://arxiv.org/abs/2207.12518

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