The Equalizer Conjecture for the Free Group of Rank Two

Alan D. Logan

doi:10.1093/qmath/haab059

The Equalizer Conjecture for the Free Group of Rank Two

Alan D. Logan^*

^*Corresponding author for this work

School of Mathematical & Computer Sciences

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

26 Downloads (Pure)

Abstract

The equalizer of a set of homomorphisms S:F(a,b)→F(Δ)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)g,h:F(Σ)→F(Δ) when the images are inert in, or retracts of, F(Δ)F(Δ)⁠.

Original language	English
Pages (from-to)	777-793
Number of pages	17
Journal	Quarterly Journal of Mathematics
Volume	73
Issue number	2
Early online date	30 Dec 2021
DOIs	https://doi.org/10.1093/qmath/haab059
Publication status	Published - Jun 2022

ASJC Scopus subject areas

General Mathematics

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The Equalizer Conjecture for the Free Group of Rank Two

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