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

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

2004-09-18

arxiv.org/abs/math/0409319v1

Mathematics

Group Theory

59 Pages, 10 figures, excerpt from thesis to be submitted for D.Phil at the University of Oxford

Scientific paper

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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