Ideal Whitehead Graphs in Out(F_r) III: Achieved Graphs in Rank 3

2013/01/29 by Pfaff, Catherine
#20F65 #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1301.7080

Abstract

By proving precisely which singularity index lists arise from the pair of invariant foliations for a pseudo-Anosov surface homeomorphism, Masur and Smillie determined a Teichmüller flow invariant stratification of the space of quadratic differentials. In this final paper of a three-paper series, we give a first step to an Out(F_r) analog of the Masur-Smillie theorem. Since the ideal Whitehead graphs defined by Handel and Mosher give a strictly finer invariant in the analogous Out(F_r) setting, we determine which of the twenty-one connected, simplicial, five-vertex graphs are ideal Whitehead graphs of fully irreducible outer automorphisms in Out(F₃).

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