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Irreducibility of a Free Group Endomorphism is a Mapping Torus Invariant

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arxiv 1910.04285 v2 pith:GHUV6KL6 submitted 2019-10-09 math.GR

classification math.GR
keywords ascendingirreducibleatoroidalendomorphismgroupinvariantextensionextensions
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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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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Irreducible Nonsurjective Endomorphisms of $F_n$ are Hyperbolic

    math.GR 2019-08 accept novelty 8.0 of 10

    Irreducible nonsurjective endomorphisms of free groups are fully irreducible and their mapping tori are word-hyperbolic.

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