Catherine Pfaff – Stratifying the Set of Fully Irreducible Elements of Out(F_r)

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Date(s) - 24 mai 2013

Catégories Pas de Catégories

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 Teichmuller flow invariant stratification of the space of quadratic differentials. 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 of a fully irreducible outer automorphism, we determined which of the twenty-one connected, simplicial, five-vertex graphs are ideal Whitehead graphs of fully irreducible outer automorphisms in $Out(F_3)$.