Forum of Mathematics, Sigma (Jan 2024)

Limit pretrees for free group automorphisms: existence

  • Jean Pierre Mutanguha

DOI
https://doi.org/10.1017/fms.2024.38
Journal volume & issue
Vol. 12

Abstract

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To any free group automorphism, we associate a real pretree with several nice properties. First, it has a rigid/non-nesting action of the free group with trivial arc stabilizers. Secondly, there is an expanding pretree-automorphism of the real pretree that represents the free group automorphism. Finally and crucially, the loxodromic elements are exactly those whose (conjugacy class) length grows exponentially under iteration of the automorphism; thus, the action on the real pretree is able to detect the growth type of an element.

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