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Detecting the growth of free group automorphisms by their action on the homology of subgroups of finite index

Adam Piggott
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Abstract

We prove that if F is a finitely generated free group and f:F -> F is an automorphism with polynomial growth of degree d, then there exists a characteristic subgroup S < F of finite index such that the induced automorphism of the abelianisation of S also grows polynomially of degree d. The proof is geometric in nature and makes use of improved relative train track representatives.

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Adam Piggott. 2004-09-18. Detecting the growth of free group automorphisms by their action on the homology of subgroups of finite index. https://arxiv.org/abs/math/0409319

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