A Generalized Axis Theorem for Cube Complexes
A Generalized Axis Theorem for Cube Complexes
复制标题
立方复形的广义轴定理
DOI：
10.2140/agt.2017.17.2737
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
Daniel J. Woodhouse
中科院分区：
文献类型：
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作者：
Daniel J. Woodhouse
我们考虑一个无逆生成的虚阿贝尔群G在CAT（0）立方复形X上正确地作用，并且没有逆.我们证明了$G$稳定一个有限维CAT（0）子复形$Y \subseteq X$是等距嵌入的组合度量。此外，我们证明了$Y$是一个产品的许多拟线。该结果代表了哈格伦德轴定理的更高维度的推广。
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.