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arXiv · 1311.4490

$Out(F_3)$ Index Realization

Catherine Pfaff
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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 Teichmueller flow invariant stratification of the space of quadratic differentials. In this paper we determine an analog to the theorem for $Out(F_3)$. That is, we determine which index lists permitted by the Gaboriau-Jaeger-Levitt-Lustig index sum inequality are achieved by fully irreducible outer automorphisms of the rank-$3$ free group.

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Catherine Pfaff. 2014-09-07. $Out(F_3)$ Index Realization. https://arxiv.org/abs/1311.4490

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