Nielsen realization by gluing: Limit groups and free products

Journal article

We generalize the Karrass–Pietrowski–Solitar and the Nielsen realization theorems from the setting of free groups to that of free products. As a result, we obtain a fixed point theorem for finite groups of outer automorphisms acting on the relative free splitting complex of Handel and Mosher and on the outer space of a free product of Guirardel and Levitt, and also a relative version of the Nielsen realization theorem, which, in the case of free groups, answers a question of Karen Vogtmann. We also prove Nielsen realization for limit groups and, as a byproduct, obtain a new proof that limit groups are CAT(0). The proofs rely on a new version of Stallings’ theorem on groups with at least two ends, in which some control over the behavior of virtual free factors is gained.

Authors: Hensel, S; Kielak, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Michigan Mathematical Journal
• Journal: Michigan Mathematical Journal
• Volume: 67
• Pages: 199-223
• Publication date: 2018-03-01
• Acceptance date: 2017-08-22
• DOI: 10.1307/mmj/1519095620
• ISSN: 0026-2285
• Language: English
• Keywords: FFR