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On finitely generated normal subgroups of Kähler groups

Francisco Nicolás

Algebraic & Geometric Topology 22 (2022) 2997–3021
DOI: 10.2140/agt.2022.22.2997

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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Kähler groups, normal subgroups, surface groups
Mathematical Subject Classification
Primary: 20F65, 32Q15
Secondary: 20E06, 20E08
Received: 19 February 2021
Revised: 3 July 2021
Accepted: 27 July 2021
Published: 13 December 2022
Francisco Nicolás
Institut de Recherche Mathématique Avancée
Université de Strasbourg