Geodesic
A generalized axis theorem for cube complexes
Woodhouse, Daniel1
1 Mathematics Department, Technion – Israel Institute of Technology, Haifa, Israel
Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 2737-2751

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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 ⊆ 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.

DOI : 10.2140/agt.2017.17.2737
Classification : 20F65
Keywords: $\mathrm{CAT}(0)$ cube complexes, geometric group theory, axis

Woodhouse, Daniel 1

1 Mathematics Department, Technion – Israel Institute of Technology, Haifa, Israel 
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Woodhouse, Daniel. A generalized axis theorem for cube complexes. Algebraic and Geometric Topology, Tome 17 (2017) no. 5, pp. 2737-2751. doi: 10.2140/agt.2017.17.2737

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