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Fully irreducible automorphisms of the free group via Dehn twisting in $\sharp_k(S^2 \times S^1)$

Funda Gültepe

Algebraic & Geometric Topology 17 (2017) 1375–1405

By using a notion of a geometric Dehn twist in k(S2 × S1), we prove that when projections of two –splittings to the free factor complex are far enough from each other in the free factor complex, Dehn twist automorphisms corresponding to the –splittings generate a free group of rank 2. Moreover, every element from this free group either is conjugate to a power of one of the Dehn twists or is a fully irreducible outer automorphism of the free group. We also prove that, when the projections of –splittings are sufficiently far away from each other in the intersection graph, the group generated by the Dehn twists has automorphisms that are either conjugate to Dehn twists or atoroidal fully irreducible.

free group, outer automorphism, Dehn twist
Mathematical Subject Classification 2010
Primary: 20F28, 20F65, 57M07
Received: 28 January 2015
Revised: 19 May 2016
Accepted: 22 June 2016
Published: 17 July 2017
Funda Gültepe
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W Green St
Urbana, IL 61801
United States