The Equalizer Conjecture for the free group of rank two

Logan, Alan David

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Date

30/12/2021

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).

Citation

Logan , A D 2021 , ' The Equalizer Conjecture for the free group of rank two ' , Quarterly Journal of Mathematics , vol. Advance Article . https://doi.org/10.1093/qmath/haab059

Publication

Quarterly Journal of Mathematics

Status

Peer reviewed

DOI

https://doi.org/10.1093/qmath/haab059

ISSN

0033-5606

Type

Journal article

Rights

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.

Description

Funding: This research was supported by Engineering and Physical Sciences Research Council (EPSRC) grant EP/R035814/1.

Collections

University of St Andrews Research

URI

http://hdl.handle.net/10023/24696