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

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

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

Group Theory 2025-02-17 v2

Authors: Naomi Andrew , Paige Hillen , Robert Alonzo Lyman , Catherine Eva Pfaff

Abstract

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.

Keywords

Out($F_3$) fully irreducible stretch factor principal element fold

Cite

@article{arxiv.2405.03681,
  title  = {Low complexity among principal fully irreducible elements of Out($F_3$)},
  author = {Naomi Andrew and Paige Hillen and Robert Alonzo Lyman and Catherine Eva Pfaff},
  journal= {arXiv preprint arXiv:2405.03681},
  year   = {2025}
}

Comments

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

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

Abstract

Keywords

Cite

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