Fully irreducible automorphisms of the free group via Dehn twisting in ♯k(S2 × S1)

Gültepe, Funda

doi:10.2140/agt.2017.17.1375

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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

DOI: 10.2140/agt.2017.17.1375

Abstract

By using a notion of a geometric Dehn twist in $♯_{k} (S^{2} \times S^{1})$ , we prove that when projections of two $ℤ$ –splittings to the free factor complex are far enough from each other in the free factor complex, Dehn twist automorphisms corresponding to the $ℤ$ –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 $ℤ$ –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.

Keywords

free group, outer automorphism, Dehn twist

Mathematical Subject Classification 2010

Primary: 20F28, 20F65, 57M07

References

Publication

Received: 28 January 2015

Revised: 19 May 2016

Accepted: 22 June 2016

Published: 17 July 2017

Authors

Funda Gültepe
Department of Mathematics University of Illinois at Urbana-Champaign 1409 W Green St Urbana, IL 61801 United States
http://www.math.illinois.edu/~fgultepe

Volume 17, issue 3 (2017)