Vol. 18, No. 1, 2020

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A note on locally elliptic actions on cube complexes

Nils Leder and Olga Varghese

Vol. 18 (2020), No. 1, 1–6
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.

Keywords
cube complexes, locally elliptic actions, global fixed points
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 51F99
Milestones
Received: 21 November 2018
Accepted: 28 November 2019
Published: 8 January 2020
Authors
Nils Leder
Department of Mathematics
Münster University
Einsteinstraße 62
48149 Münster
Germany
Olga Varghese
Department of Mathematics
Münster University
Einsteinstraße 62
48149 Münster
Germany