On finitely generated normal subgroups of Kähler groups

Francisco Nicolás (1)

1 IRMA - Institut de Recherche Mathématique Avancée

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 non-trivial 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.

Domaines: Mathématiques [math]

Francisco Nicolás. On finitely generated normal subgroups of Kähler groups. Algebraic and Geometric Topology, In press. ⟨hal-03462622⟩