# Counting Growth Types of Automorphisms of Free Groups

@article{Levitt2008CountingGT, title={Counting Growth Types of Automorphisms of Free Groups}, author={Gilbert Levitt}, journal={Geometric and Functional Analysis}, year={2008}, volume={19}, pages={1119-1146} }

Given an automorphism of a free group Fn, we consider the following invariants: e is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); d is the maximal degree of polynomial growth of conjugacy classes; R is the rank of the fixed subgroup. We determine precisely which triples (e, d, R) may be realized by an automorphism of Fn. In particular, the inequality $${{e \leq \frac{3n-2}{4}}}$$ (due to Levitt–Lustig) always holds… CONTINUE READING

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