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 |
---|---|
Journal | Mathematical Research Letters |
Publication status | Accepted/In press - 9 Aug 2022 |
Keywords
- math.GR
- 20F65 (Primary) 57M10, 20F05, 20F67, 20J05 (Secondary)