Fully irreducible Automorphisms of the Free Group via Dehn twisting in   $\sharp_k(S^2 \times S^1)$
  By using a notion of a geometric Dehn twist in $\sharp_k(S^2 \times S^1)$, we prove that when projections of two $\mathbb{Z}$-splittings to the free factor complex are far enough from each other in the free factor complex, Dehn twist automorphisms corresponding to the $\mathbb{Z}$-splittings generate a free group of rank $2$. Moreover, every element from this free group is either conjugate to a power of one of the Dehn twists or it is a fully irreducible outer automorphism of the free group. We also prove that, when projected to the intersection graph, the same group of Dehn twists produce atoroidal fully irreducible automorphisms. 
Funda G\"ultepe
math.GR math.GT