The Surface Group Conjectures for groups with two generators
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.
Citation
Gardam , G , Kielak , D & Logan , A D 2022 , ' The Surface Group Conjectures for groups with two generators ' , Mathematical Research Letters . < https://arxiv.org/abs/2202.11093 >
Publication
Mathematical Research Letters
Status
Peer reviewed
ISSN
1073-2780Type
Journal article
Rights
Copyright © 2022 International Press of Boston, Inc. All rights reserved. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://www.intlpress.com/site/pub/pages/journals/items/mrl/_home/_main/index.php
Description
Funding: 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.Collections
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