Order-Preserving outer automorphisms of free and surface groups

2025/01/31 by Johnson, Jonathan, Le, Khanh
#20F28 #20F60 #Commutative Algebra (math.AC) #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2501.18847

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.

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