The surface group conjectures for groups with two generators

DOI10.4310/MRL.2023.V30.N1.A5zbMATH Open1517.20066arXiv2202.11093OpenAlexW4381488482WikidataQ123194280 ScholiaQ123194280MaRDI QIDQ6100648

Giles Gardam, Dawid Kielak, Alan D. Logan

Publication date: 22 June 2023

Published in: Mathematical Research Letters (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/2202.11093

zbMATH Keywords

free groupsurface groupone-relator groupresidually finite groupMel'nikov group

Mathematics Subject Classification ID

Covering spaces and low-dimensional topology (57M10) Generators, relations, and presentations of groups (20F05) Geometric group theory (20F65) Homological methods in group theory (20J05) Hyperbolic groups and nonpositively curved groups (20F67)

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