On finitely generated normal subgroups of K\"ahler groups

Francisco Nicolás

doi:10.2140/agt.2022.22.2997

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arXiv · 2102.01128

On finitely generated normal subgroups of K\"ahler groups

Francisco Nicolás

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Abstract

We prove that if a surface group embeds as a normal subgroup in a K\"ahler group and the conjugation action of the K\"ahler group on the surface group preserves the conjugacy class of a non-trivial element, then the K\"ahler 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 K\"ahler group then it is virtually a surface group. More generally we give restrictions on normal subgroups of K\"ahler groups which are amalgamated products or HNN extensions.

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Francisco Nicolás. 2021-02-01. On finitely generated normal subgroups of K\"ahler groups. https://doi.org/10.2140/agt.2022.22.2997

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