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Hyperbolic Immersions of Free Groups

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arxiv 1809.04761 v2 pith:L3NPNQJU submitted 2018-09-13 math.GR

Jean Pierre Mutanguha This is my paper · ORCID
classification math.GR
keywords endomorphismsinjectivetheoremappliesbaumslag-solitarcorrespondingendomorphismextending
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abstract

We prove that the mapping torus of a graph immersion has a word-hyperbolic fundamental group if and only if the corresponding endomorphism does not produce Baumslag-Solitar subgroups. Due to a result by Reynolds, this theorem applies to all injective endomorphisms of $F_2$ and nonsurjective fully irreducible endomorphisms of $F_n$. We also give a framework for extending the theorem to all injective endomorphisms of $F_n$.

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  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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