Stable representatives for symmetric automorphisms of groups and the general form of the Scott conjecture

Sykiotis, Mihalis

doi:10.1090/S0002-9947-03-03385-3

Stable representatives for symmetric automorphisms of groups and the general form of the Scott conjecture
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Trans. Amer. Math. Soc. 356 (2004), 2405-2441 Request permission

Abstract:

Let $G$ be a group acting on a tree $X$ such that all edge stabilizers are finite. We extend Bestvina-Handel’s theory of train tracks for automorphisms of free groups to automorphisms of $G$ which permute vertex stabilizers. Using this extension we show that there is an upper bound depending only on $G$ for the complexity of the graph of groups decomposition of the fixed subgroups of such automorphisms of $G$.

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