A Generalized Axis Theorem for Cube Complexes

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.

arXiv comment14 pages Corrected proof of Corollary 1.4. Various other corrections made following referee report and comments made by thesis examiner. Appendix added giving a proof of a theorem by Gerasimov

References in corpus (1)

• Rank rigidity for CAT(0) cube complexes

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