@article{3f663b98c6e9410ca0b207383777467c,
title = "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.",
keywords = "One-relator group, Surface group",
author = "Giles Gardam and Dawid Kielak and Logan, {Alan D.}",
note = "Funding: This work has received funding from the European Research Council (ERC) under the European Union{\textquoteright}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{\textquoteright}s Excellence Strategy EXC 2044–390685587, Mathematics M{\"u}nster: Dynamics–Geometry–Structure.",
year = "2023",
month = jun,
day = "21",
doi = "10.4310/mrl.2023.v30.n1.a5",
language = "English",
volume = "30",
pages = "109--123",
journal = "Mathematical Research Letters",
issn = "1073-2780",
publisher = "International Press of Boston, Inc.",
number = "1",
}