The equalizer conjecture for the free group of rank two

Alan D. Logan

The equalizer conjecture for the free group of rank two

Group Theory 2021-11-10 v3

Authors: Alan D. Logan

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, $F(\Delta)$ .

Keywords

equaliser conjecture free group homomorphisms rank inert subgroup retract

Cite

@article{arxiv.2003.05270,
  title  = {The equalizer conjecture for the free group of rank two},
  author = {Alan D. Logan},
  journal= {arXiv preprint arXiv:2003.05270},
  year   = {2021}
}

Comments

19 pages. v2 incorporates minor edits (mostly typos). v3 is the final version accepted for publication, with improved structural and algorithmic results for retracts

The equalizer conjecture for the free group of rank two

Abstract

Keywords

Cite

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