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The Surface Group Conjectures for groups with two generators

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dc.contributor.authorGardam, Giles
dc.contributor.authorKielak, Dawid
dc.contributor.authorLogan, Alan D.
dc.date.accessioned2023-01-04T15:30:02Z
dc.date.available2023-01-04T15:30:02Z
dc.date.issued2023-06-21
dc.identifier280886955
dc.identifier3f663b98-c6e9-410c-a0b2-07383777467c
dc.identifier.citationGardam , G , Kielak , D & Logan , A D 2023 , ' The Surface Group Conjectures for groups with two generators ' , Mathematical Research Letters , vol. 30 , no. 1 , pp. 109-123 . https://doi.org/10.4310/mrl.2023.v30.n1.a5en
dc.identifier.issn1073-2780
dc.identifier.urihttps://hdl.handle.net/10023/26667
dc.descriptionFunding: This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant agreement No. 850930), and from the Engineering and Physical Sciences Research Council (EPSRC), grants EP/R035814/1 and EP/S010963/1, and was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project ID 427320536 – SFB 1442, as well as under Germany’s Excellence Strategy EXC 2044–390685587, Mathematics Münster: Dynamics–Geometry–Structure.en
dc.description.abstractThe 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.
dc.format.extent15
dc.format.extent192829
dc.language.isoeng
dc.relation.ispartofMathematical Research Lettersen
dc.subjectOne-relator groupen
dc.subjectSurface groupen
dc.subjectQA Mathematicsen
dc.subjectT-NDASen
dc.subjectMCCen
dc.subject.lccQAen
dc.titleThe Surface Group Conjectures for groups with two generatorsen
dc.typeJournal articleen
dc.contributor.institutionUniversity of St Andrews. Pure Mathematicsen
dc.identifier.doi10.4310/mrl.2023.v30.n1.a5
dc.description.statusPeer revieweden
dc.identifier.urlhttps://www.intlpress.com/site/pub/pages/journals/items/mrl/_home/acceptedpapers/index.phpen
dc.identifier.urlhttps://arxiv.org/abs/2202.11093en


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