When is a polynomially growing automorphism of F_n geometric ?

2016/05/24 by Kaidi Ye, Ye, Kaidi
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Automorphism #Automorphism group #Combinatorics #Discrete mathematics #FOS: Mathematics #Geometric and Algebraic Topology #Geometry #Graph #Group Theory (math.GR) #Iterated function #Mathematical analysis #Mathematics #Order (exchange) #Twist #math.GR #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1605.07390

arxiv created 2016/05/24 · openalex publication_date 2016/05/24 · arxiv updated 2016/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of this paper is an algorithmic answer to the question raised in the title, up to replacing the given ϕ ∈ Out(F_n) by a positive power. In order to provide this algorithm, it is shown that every polynomially growing automorphism ϕ can be represented by an iterated Dehn twist on some graph-of-groups \calG with π₁\calG = F_n. One then uses results of two previous papers \citeKY01, KY02 as well as some classical results such as the Whitehead algorithm to prove the claim.

Citations

• Train Tracks and Automorphisms of Free Groups
• Partial Dehn twists of free groups relative to local Dehn twists - a dichotomy

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