Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group

2025/11/19 by Seo, Donggyun
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems

paper · doi:10.48550/arxiv.2511.15063

openalex publication_date 2025/11/19 · openalex created_date 2025/11/23 · openalex updated_date 2026/07/28

Abstract

We study Dehn twists in the outer automorphism group of a finitely generated non-abelian free group. Our main result states that, under certain compatibility conditions, sufficiently large powers of finitely many Dehn twists generate a right-angled Artin group. The proof proceeds by analyzing the geometry of spheres, tori, and simple closed curves in a doubled handlebody. Along the way, we establish the bigon--bihedron criterion and an equivalent condition for commuting Dehn twists. Furthermore, we construct a compact topological space on which every Dehn twist acts parabolically.

Citations

• Right-angled Artin groups and a generalized isomorphism problem for\n finitely generated subgroups of mapping class groups
• Twisting out fully irreducible automorphisms

Related

• Subgroups of the mapping class group of the torus generated by powers of Dehn twists
• Normal form and parabolic dynamics for quadratically growing automorphisms of free groups
• Twisting out fully irreducible automorphisms
• Partial Dehn twists of free groups relative to local Dehn twists - a dichotomy
• The Dehn twist coefficient for big and small mapping class groups