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arXiv · 2202.11093

The Surface Group Conjectures for groups with two generators

Giles Gardam·Dawid Kielak·Alan D. Logan
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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.

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Giles Gardam, Dawid Kielak, Alan D. Logan. 2022-02-22. The Surface Group Conjectures for groups with two generators. https://arxiv.org/abs/2202.11093

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