English

Ideal Whitehead Graphs in Out(F_r) II: The Complete Graph in Each Rank

Group Theory 2014-09-09 v2 Geometric Topology

Abstract

We show how to construct, for each r3r \geq 3, an ageometric, fully irreducible ϕOut(Fr)\phi\in Out(F_r) whose ideal Whitehead graph is the complete graph on 2r12r-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 ϕOut(F3)\phi \in Out(F_3). The result is a first step to an Out(Fr)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 ϕOut(Fr)\phi\in Out(F_r)

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