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.
Original languageEnglish
JournalMathematical Research Letters
Publication statusAccepted/In press - 9 Aug 2022

Keywords

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

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