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 | |
Publication status | Published - 21 Jun 2023 |
Keywords
- math.GR
- 20F65 (Primary) 57M10, 20F05, 20F67, 20J05 (Secondary)