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arXiv · 1701.02505

Essential surfaces in graph pairs

Henry Wilton
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Abstract

A well known question of Gromov asks whether every one-ended hyperbolic group $Γ$ has a surface subgroup. We give a positive answer when $Γ$ is the fundamental group of a graph of free groups with cyclic edge groups. As a result, Gromov's question is reduced (modulo a technical assumption on 2-torsion) to the case when $Γ$ is rigid. We also find surface subgroups in limit groups. It follows that a limit group with the same profinite completion as a free group must in fact be free, which answers a question of Remeslennikov in this case.

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Henry Wilton. 2018-05-09. Essential surfaces in graph pairs. https://arxiv.org/abs/1701.02505

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