Low complexity among principal fully irreducible elements of Out($F_3$)

Abstract

We find the shortest realized stretch factor for a fully irreducible $\phi \in \mathrm{Out}(F_3)$ and show that it is realized by a "principal" fully irreducible element. We also show that it is the only principal fully irreducible produced by a single fold in any rank.

22 pages, one large and many small diagrams. Final version, accepted at Algebraic & Geometric Topology