The Equalizer Conjecture for the free group of rank two

Alan David Logan

doi:10.1093/qmath/haab059

The Equalizer Conjecture for the free group of rank two

Alan David Logan

Pure Mathematics

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Abstract

The equalizer of a set of homomorphisms S : F(a,b) → F(Δ) has rank at most two if S contains an injective map and is not finitely generated otherwise. This proves a strong form of Stallings’ Equalizer Conjecture for the free group of rank two. Results are also obtained for pairs of homomorphisms g,h : F(Σ) → F(Δ) when the images are inert in, or retracts of, F(Δ).

Original language	English
Number of pages	17
Journal	Quarterly Journal of Mathematics
Volume	Advance Article
DOIs	https://doi.org/10.1093/qmath/haab059
Publication status	Published - 30 Dec 2021

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Copyright © The Author(s) 2021. Published by Oxford University Press. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
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Cite this

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abstract = "The equalizer of a set of homomorphisms S : F(a,b) → F(Δ) has rank at most two if S contains an injective map and is not finitely generated otherwise. This proves a strong form of Stallings{\textquoteright} Equalizer Conjecture for the free group of rank two. Results are also obtained for pairs of homomorphisms g,h : F(Σ) → F(Δ) when the images are inert in, or retracts of, F(Δ).",

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N2 - The equalizer of a set of homomorphisms S : F(a,b) → F(Δ) has rank at most two if S contains an injective map and is not finitely generated otherwise. This proves a strong form of Stallings’ Equalizer Conjecture for the free group of rank two. Results are also obtained for pairs of homomorphisms g,h : F(Σ) → F(Δ) when the images are inert in, or retracts of, F(Δ).

AB - The equalizer of a set of homomorphisms S : F(a,b) → F(Δ) has rank at most two if S contains an injective map and is not finitely generated otherwise. This proves a strong form of Stallings’ Equalizer Conjecture for the free group of rank two. Results are also obtained for pairs of homomorphisms g,h : F(Σ) → F(Δ) when the images are inert in, or retracts of, F(Δ).

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The Equalizer Conjecture for the free group of rank two

Abstract

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