The Surface Group Conjectures for groups with two generators
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...
| Main Authors: | , , |
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| Format: | Journal article |
| Language: | English |
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International Press
2023
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| _version_ | 1797110512642686976 |
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| author | Gardam, G Kielak, D Logan, AD |
| author_facet | Gardam, G Kielak, D Logan, AD |
| author_sort | Gardam, G |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-07T07:57:23Z |
| format | Journal article |
| id | oxford-uuid:570dc8a2-fd5e-46c9-a0c7-7d442a50dd15 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:57:23Z |
| publishDate | 2023 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:570dc8a2-fd5e-46c9-a0c7-7d442a50dd152023-08-24T14:34:44ZThe Surface Group Conjectures for groups with two generatorsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:570dc8a2-fd5e-46c9-a0c7-7d442a50dd15EnglishSymplectic ElementsInternational Press2023Gardam, GKielak, DLogan, ADThe 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. |
| spellingShingle | Gardam, G Kielak, D Logan, AD The Surface Group Conjectures for groups with two generators |
| title | The Surface Group Conjectures for groups with two generators |
| title_full | The Surface Group Conjectures for groups with two generators |
| title_fullStr | The Surface Group Conjectures for groups with two generators |
| title_full_unstemmed | The Surface Group Conjectures for groups with two generators |
| title_short | The Surface Group Conjectures for groups with two generators |
| title_sort | surface group conjectures for groups with two generators |
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