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March 2018 Nielsen Realization by Gluing: Limit Groups and Free Products
Sebastian Hensel, Dawid Kielak
Michigan Math. J. 67(1): 199-223 (March 2018). DOI: 10.1307/mmj/1519095620

Abstract

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.

Citation

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Sebastian Hensel. Dawid Kielak. "Nielsen Realization by Gluing: Limit Groups and Free Products." Michigan Math. J. 67 (1) 199 - 223, March 2018. https://doi.org/10.1307/mmj/1519095620

Information

Received: 19 September 2016; Revised: 22 August 2017; Published: March 2018
First available in Project Euclid: 20 February 2018

zbMATH: 06965596
MathSciNet: MR3770860
Digital Object Identifier: 10.1307/mmj/1519095620

Subjects:
Primary: 20F65
Secondary: 20E06

Rights: Copyright © 2018 The University of Michigan

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Vol.67 • No. 1 • March 2018
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