English

$Out(F_3)$ Index Realization

Group Theory 2014-09-09 v2 Geometric Topology

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(F3)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-33 free group.

Cite

@article{arxiv.1311.4490,
  title  = {$Out(F_3)$ Index Realization},
  author = {Catherine Pfaff},
  journal= {arXiv preprint arXiv:1311.4490},
  year   = {2014}
}

Comments

Readability improved & paper expanded to include more background on how the examples can be verified

R2 v1 2026-06-22T02:09:49.585Z