Counting Growth Types of Automorphisms of Free Groups

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 fi...

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Bibliographic Details
Published in:Geometric and functional analysis 2009-12, Vol.19 (4), p.1119-1146
Main Author: Levitt, Gilbert
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary: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 (due to Levitt–Lustig) always holds. In an appendix, we show that any conjugacy class grows like a polynomial times an exponential under iteration of the automorphism.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-009-0016-4