A note on locally elliptic actions on cube complexes

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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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

Vol. 18, No. 1, 2020

Nils Leder and Olga Varghese

Abstract

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors