Download this article
Download this article For screen
For printing
Recent Issues

Volume 22
Issue 6, 2533–3057
Issue 5, 2007–2532
Issue 4, 1497–2006
Issue 3, 991–1495
Issue 2, 473–990
Issue 1, 1–472

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editorial Interests
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Author Index
To Appear
 
Other MSP Journals
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