Catherine Pfaff
Published 2013-01-28, updated 2014-09-07Version 2
We show how to construct, for each $r \geq 3$, an ageometric, fully irreducible $\phi\in Out(F_r)$ whose ideal Whitehead graph is the complete graph on $2r-1$ vertices. This paper is the second in a series of three where we show that precisely eighteen of the twenty-one connected, simplicial, five-vertex graphs are ideal Whitehead graphs of fully irreducible $\phi \in Out(F_3)$. The result is a first step to an $Out(F_r)$ version of the Masur-Smillie theorem proving precisely which index lists arise from singular measured foliations for pseudo-Anosov mapping classes. In this paper we additionally give a method for finding periodic Nielsen paths and prove a criterion for identifying representatives of ageometric, fully irreducible $\phi\in Out(F_r)$
Comments: The main revisions are to fill in missing conditions on rotationlessness. In particular, a power should have been taken of the map giving the main theorem. However, Remark 4.3 also needed to be adjusted. There was also a confusing typo in the ideal decomposition proposition that needed to be fixed
Ideal Whitehead Graphs in Out(F_r) I: Some Unachieved Graphs
Ideal Whitehead Graphs in Out(F_r) III: Achieved Graphs in Rank 3
A train track directed random walk on $Out(F_r)$
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