Ideal Whitehead Graphs in Out(F_r) II: The Complete Graph in Each Rank
Abstract
We show how to construct, for each , an ageometric, fully irreducible whose ideal Whitehead graph is the complete graph on 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 . The result is a first step to an 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
Keywords
Cite
@article{arxiv.1301.6645,
title = {Ideal Whitehead Graphs in Out(F_r) II: The Complete Graph in Each Rank},
author = {Catherine Pfaff},
journal= {arXiv preprint arXiv:1301.6645},
year = {2014}
}
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