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arXiv · 2306.05941

Rigidity of the free factor complex

Mladen Bestvina·Martin R Bridson
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Abstract

We establish the following non-abelian analogue of the Fundamental Theorem of Projective Geometry: the natural map from ${\rm{Aut}}(F_n)$ to the automorphism group of the free-factor complex $\mathcal{AF}_n$ is an isomorphism. We also prove the corresponding theorem for the action of ${\rm{Out}}(F_n)$ on the complex of conjugacy classes of free factors.

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Mladen Bestvina, Martin R Bridson. 2023-06-09. Rigidity of the free factor complex. https://arxiv.org/abs/2306.05941

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