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