Order-Preserving outer automorphisms of free and surface groups

Jonathan Johnson; Khanh Le

Order-Preserving outer automorphisms of free and surface groups

Group Theory 2026-04-24 v2 Commutative Algebra Rings and Algebras

Authors: Jonathan Johnson , Khanh Le

Abstract

We give a complete classification to when a finite group of outer automorphisms preserves a bi-order on a non-abelian free group and bi-orderable surface groups. We also give another new criterion for an outer automorphism of $F_n$ induced by action of an $n$ -strand braid to preserve a bi-order on $F_n.$ Using the new criterion, we produce examples of order-preserving whose underlying permutation is a full cycle which answers in affirmative a question of Kin and Rolfsen.

Keywords

automorphism groups automorphisms of algebraic surfaces braid groups

Cite

@article{arxiv.2501.18847,
  title  = {Order-Preserving outer automorphisms of free and surface groups},
  author = {Jonathan Johnson and Khanh Le},
  journal= {arXiv preprint arXiv:2501.18847},
  year   = {2026}
}

Comments

25 pages. Revised according to comments from the referees. The exposition in Section 2 was largely rewritten. Section 4.1 was removed. More details added to section 5.1. To appear in Journal of Algebra

Order-Preserving outer automorphisms of free and surface groups

Abstract

Keywords

Cite

Comments

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