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

Catherine Eva Pfaff; Naomi Andrew; Paige Hillen; Robert Alonzo Lyman

arxiv: 2405.03681 · v2 · pith:LRYIMLKAnew · submitted 2024-05-06 · 🧮 math.GR

Low complexity among principal fully irreducible elements of Out(F₃)

Naomi Andrew , Paige Hillen , Robert Alonzo Lyman , Catherine Eva Pfaff This is my paper

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keywords fullyirreducibleprincipalrealizedcomplexityelementelementsfactor

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We find the shortest realized stretch factor for a fully irreducible $\varphi\in\mathrm{Out}(F_3)$ 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.

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Low complexity among principal fully irreducible elements of Out(F₃)

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