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• W2573540693 abstract "A well-known question of Gromov asks whether every one-ended hyperbolic group <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Gamma> <mml:semantics> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:annotation encoding=application/x-tex>Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> has a surface subgroup. We give a positive answer when <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Gamma> <mml:semantics> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:annotation encoding=application/x-tex>Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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 <inline-formula content-type=math/mathml> <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=normal upper Gamma> <mml:semantics> <mml:mi mathvariant=normal>Γ<!-- Γ --></mml:mi> <mml:annotation encoding=application/x-tex>Gamma</mml:annotation> </mml:semantics> </mml:math> </inline-formula> 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." @default.
• W2573540693 created "2017-01-26" @default.
• W2573540693 creator A5078785560 @default.
• W2573540693 date "2018-06-18" @default.
• W2573540693 modified "2023-10-14" @default.
• W2573540693 title "Essential surfaces in graph pairs" @default.
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• W2573540693 doi "https://doi.org/10.1090/jams/901" @default.
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