On finitely generated normal subgroups of K\"ahler groups

DOI10.2140/AGT.2022.22.2997arXiv2102.01128MaRDI QIDQ6359599

Publication date: 1 February 2021

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.

Mathematics Subject Classification ID

Geometric group theory (20F65) Kähler manifolds (32Q15) Free products of groups, free products with amalgamation, Higman-Neumann-Neumann extensions, and generalizations (20E06) Groups acting on trees (20E08)

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