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arXiv · 1412.8582

Mapping tori of free group automorphisms, and the Bieri-Neumann-Strebel invariant of graphs of groups

Christopher H. Cashen·Gilbert Levitt
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Abstract

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.

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Christopher H. Cashen, Gilbert Levitt. 2014-12-30. Mapping tori of free group automorphisms, and the Bieri-Neumann-Strebel invariant of graphs of groups. https://doi.org/10.1515/jgth-2015-0038

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