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2020 A note on locally elliptic actions on cube complexes
Nils Leder, Olga Varghese
Innov. Incidence Geom. Algebr. Topol. Comb. 18(1): 1-6 (2020). DOI: 10.2140/iig.2020.18.1

Abstract

We deduce from Sageev’s results that whenever a group acts locally elliptically on a finite-dimensional CAT(0) cube complex, then it must fix a point. As an application, we partially prove a conjecture by Marquis concerning actions on buildings and we give an example of a group G such that G does not have property (T), but G and all its finitely generated subgroups can not act without a fixed point on a finite-dimensional CAT(0) cube complex, answering a question by Barnhill and Chatterji.

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Nils Leder. Olga Varghese. "A note on locally elliptic actions on cube complexes." Innov. Incidence Geom. Algebr. Topol. Comb. 18 (1) 1 - 6, 2020. https://doi.org/10.2140/iig.2020.18.1

Information

Received: 21 November 2018; Accepted: 28 November 2019; Published: 2020
First available in Project Euclid: 26 November 2020

MathSciNet: MR4162939
Digital Object Identifier: 10.2140/iig.2020.18.1

Subjects:
Primary: 20F65
Secondary: 51F99

Rights: Copyright © 2020 Mathematical Sciences Publishers

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