On finitely generated normal subgroups of K\"ahler groups
Geometric Topology
2022-12-21 v2 Algebraic Geometry
Group Theory
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.
Cite
@article{arxiv.2102.01128,
title = {On finitely generated normal subgroups of K\"ahler groups},
author = {Francisco Nicolás},
journal= {arXiv preprint arXiv:2102.01128},
year = {2022}
}
Comments
19 pages, v2: this is the final version, accepted in Algebraic and Geometric Topology