Free-group automorphisms, train tracks and the beaded decomposition

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dc.creatorBridson, Martin R.
dc.creatorGroves, Daniel
dc.date2005-07-28
dc.date2006-07-28
dc.date.accessioned2026-07-07T06:42:43Z
dc.date.available2026-07-07T06:42:43Z
dc.descriptionWe study the automorphisms ϕof a finitely generated free group F. Building on the train-track technology of Bestvina, Feighn and Handel, we provide a topological representative f:G\to G of a power of ϕthat behaves very much like the realization on the rose of a positive automorphism. This resemblance is encapsulated in the Beaded Decomposition Theorem which describes the structure of paths in G obtained by repeatedly passing to f-images of an edge and taking subpaths. This decomposition is the key to adapting our proof of the quadratic isoperimetric inequality for $F\rtimes_ϕ\mathbb Z$, with ϕpositive, to the general case. To illustrate the wider utility of our topological normal form, we provide a short proof that for every w in F, the function $n\mapsto |ϕ^n(w)|$ grows either polynomially or exponentially.
dc.descriptionVersion 2 is 35 pages. The section on growth contained an error pointed out by Gilbert Levitt, and has been removed. A corrected verion will appear in a subsequent paper. Otherwise, changes are mostly cosmetic
dc.identifierhttps://arxiv.org/abs/math/0507589
dc.identifierhttp://arxiv.org/abs/math/0507589
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/102143
dc.subjectGroup Theory
dc.subject20F65; 20F06, 20F28, 57M07
dc.titleFree-group automorphisms, train tracks and the beaded decomposition
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