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On finitely generated
normal subgroups of Kähler groups
Francisco Nicolás |
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Algebraic & Geometric Topology 22 (2022) 2997–3021
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DOI: 10.2140/agt.2022.22.2997
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Abstract |
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We prove that if a surface group embeds as a normal subgroup in a Kähler group and the conjugation action of the Kähler group on the surface group preserves the conjugacy class of a nontrivial element, then the Kähler group is virtually given by a direct product, where one factor is a surface group. Moreover we prove that if a one-ended hyperbolic group with infinite outer automorphism group embeds as a normal subgroup in a Kähler group, then it is virtually a surface group. More generally, we give restrictions on normal subgroups of Kähler groups which are amalgamated products or HNN extensions. |
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Keywords
Kähler groups, normal subgroups, surface groups
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Mathematical Subject Classification
Primary: 20F65, 32Q15
Secondary: 20E06, 20E08
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References |
Publication
Received: 19 February 2021
Revised: 3 July 2021
Accepted: 27 July 2021
Published: 13 December 2022
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Authors |
| Francisco Nicolás | |
| Institut de Recherche Mathématique
Avancée Université de Strasbourg Strasbourg France |
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