A generalized axis theorem for cube complexes

Woodhouse, Daniel

doi:10.2140/agt.2017.17.2737

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A generalized axis theorem for cube complexes

Daniel J Woodhouse

Algebraic & Geometric Topology 17 (2017) 2737–2751

DOI: 10.2140/agt.2017.17.2737

Abstract

We consider a finitely generated virtually abelian group $G$ acting properly and without inversions on a $CAT (0)$ cube complex $X$ . We prove that $G$ stabilizes a finite-dimensional $CAT (0)$ subcomplex $Y \subseteq X$ that is isometrically embedded in the combinatorial metric. Moreover, we show that $Y$ is a product of finitely many quasilines. The result represents a higher-dimensional generalization of Haglund’s axis theorem.

Keywords

$\mathrm{CAT}(0)$ cube complexes, geometric group theory, axis

Mathematical Subject Classification 2010

Primary: 20F65

References

Publication

Received: 3 February 2016

Revised: 9 May 2017

Accepted: 8 April 2017

Published: 19 September 2017

Authors

Daniel J Woodhouse
Mathematics Department Technion – Israel Institute of Technology Haifa Israel

Volume 17, issue 5 (2017)