The Surface Group Conjectures for groups with two generators
Group Theory
2022-08-10 v2
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.
Cite
@article{arxiv.2202.11093,
title = {The Surface Group Conjectures for groups with two generators},
author = {Giles Gardam and Dawid Kielak and Alan D. Logan},
journal= {arXiv preprint arXiv:2202.11093},
year = {2022}
}
Comments
14 pages, final version accepted for publication