The Surface Group Conjectures for groups with two generators

Giles Gardam; Dawid Kielak; Alan D. Logan

doi:10.4310/MRL.2023.v30.n1.a5

The Surface Group Conjectures for groups with two generators

Giles Gardam, Dawid Kielak, Alan D. Logan

School of Engineering & Physical Sciences

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Abstract

The Surface Group Conjectures are statements about recognising surface groups among one-relator groups, using either the structure of their finite-index subgroups, or all subgroups. We resolve these conjectures in the two generator case. More generally, we prove that every two-generator one-relator group with every infinite-index subgroup free is itself either free or a surface group.

Original language	English
Pages (from-to)	109–123
Number of pages	15
Journal	Mathematical Research Letters
Volume	30
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2023.v30.n1.a5
Publication status	Published - 21 Jun 2023

Keywords

math.GR
20F65 (Primary) 57M10, 20F05, 20F67, 20J05 (Secondary)

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The Surface Group Conjectures for groups with two generators

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