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

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.

38 pages, 7 figures. v4: substantial revision. Sections 3 and 5 rewritten with new results on intersection circles (Lemmas 3.3, 3.7); the compatibility condition and the constant in the main theorem are changed; Section 6 is extended from single twists to multi-twists (Theorems 1.4, 1.5)