On finitely generated normal subgroups of Kähler groups

Nicolás, Francisco

doi:10.2140/agt.2022.22.2997

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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

Abstract

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.

Keywords

Kähler groups, normal subgroups, surface groups

Mathematical Subject Classification

Primary: 20F65, 32Q15

Secondary: 20E06, 20E08

References

Publication

Received: 19 February 2021

Revised: 3 July 2021

Accepted: 27 July 2021

Published: 13 December 2022

Authors

Francisco Nicolás
Institut de Recherche Mathématique Avancée Université de Strasbourg Strasbourg France

Volume 22, issue 6 (2022)