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arXiv · 2003.05270

The equalizer conjecture for the free group of rank two

Alan D. Logan
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Abstract

The equaliser of a set of homomorphisms $S: F(a, b)\rightarrow F(\Delta)$ has rank at most two if $S$ contains an injective map, and is not finitely generated otherwise. This proves a strong form of Stallings' Equaliser Conjecture for the free group of rank two. Results are also obtained for pairs of homomorphisms $g, h:F(\Sigma)\rightarrow F(\Delta)$ when the images are inert in, or retracts of, $F(\Delta)$.

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Alan D. Logan. 2020-03-11. The equalizer conjecture for the free group of rank two. https://arxiv.org/abs/2003.05270

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