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Low complexity among
principal fully irreducible elements of
$\mathrm{Out}(F_3)$
Naomi Andrew, Paige Hillen, Robert Alonzo Lyman and Catherine Eva Pfaff |
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Algebraic & Geometric Topology 26 (2026) 2157–2180
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Abstract |
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We find the shortest realized stretch factor for a fully irreducible and show that it is realized by a “principal” fully irreducible element. We also show that it is the only principal fully irreducible outer automorphism in any rank produced by a single fold. |
Keywords
outer automorphisms of free groups, train track map, outer
space, laminations, Perron–Frobenius
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Mathematical Subject Classification
Primary: 20E05, 20F65
Secondary: 20E08, 20E36, 20F28
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References |
Publication
Received: 7 May 2024
Revised: 15 January 2025
Accepted: 9 February 2025
Published: 22 June 2026
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Authors |
| Naomi Andrew | |
| Mathematical Institute University of Oxford Oxford United Kingdom |
Université Paris-Saclay, CNRS Laboratoire de mathématiques d’Orsay Orsay France |
| https://naomigandrew.wordpress.com | |
| Paige Hillen | |
| Department of Mathematics University of California Santa Barbara Santa Barbara, CA United States |
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| https://sites.google.com/view/paigehillen/home | |
| Robert Alonzo Lyman | |
| Department of Mathematics Rutgers University–Newark Newark, NJ United States |
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| https://robbielyman.com/math | |
| Catherine Eva Pfaff | |
| Department of Mathematics and
Statistics Queen’s University Kingston, ON Canada |
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| https://catherinepfaff.com/ | |
| © 2026 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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