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arXiv · 1910.04285

Irreducibility of a Free Group Endomorphism is a Mapping Torus Invariant

Jean Pierre Mutanguha
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Abstract

We prove that the property of a free group endomorphism being irreducible is a group invariant of the ascending HNN extension it defines. This answers a question posed by Dowdall-Kapovich-Leininger. We further prove that being irreducible and atoroidal is a commensurability invariant. The invariance follows from an algebraic characterization of ascending HNN extensions that determines exactly when their defining endomorphisms are irreducible and atoroidal; specifically, we show that the endomorphism is irreducible and atoroidal if and only if the ascending HNN extension has no infinite index subgroups that are ascending HNN extensions.

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Jean Pierre Mutanguha. 2019-10-09. Irreducibility of a Free Group Endomorphism is a Mapping Torus Invariant. https://doi.org/10.4171/cmh/506

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