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arXiv · 2511.15063

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

Donggyun Seo
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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 multi-twists act parabolically, fixing simplices of weighted multicores, and fully irreducible elements act with north-south dynamics.

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Donggyun Seo. 2025-11-19. Dynamics of Dehn Twists in the Outer Automorphism Group of a Free Group. https://arxiv.org/abs/2511.15063

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