%0 Journal Article
%T Mapping tori of free group automorphisms, and the Bieri-Neumann-Strebel invariant of graphs of groups
%A Christopher H. Cashen
%A Gilbert Levitt
%J Mathematics
%D 2014
%I arXiv
%X Let $G$ be the mapping torus of a polynomially growing automorphism of a finitely generated free group. We determine which epimorphisms from $G$ to $\mathbb{Z}$ have finitely generated kernel, and we compute the rank of the kernel. We thus describe all possible ways of expressing $G$ as the mapping torus of a free group automorphism. This is similar to the case for 3--manifold groups, and different from the case of mapping tori of exponentially growing free group automorphisms. The proof uses a hierarchical decomposition of $G$ and requires determining the Bieri-Neumann-Strebel invariant of the fundamental group of certain graphs of groups.
%U http://arxiv.org/abs/1412.8582v1