余紧立方化的粗障碍
Coarse obstructions to cocompact cubulation
AI总结：
本文利用 CAT(0) 立方复形大尺度维数界的冲突建立粗障碍，排除群的余紧立方化乃至粗中位数性质，并给出自由群-by-循环群、管状群及首个不可余紧立方化的 C(6) 群等应用。
摘要：
我们提供几何方法，用于界定与给定群 G 拟等距的 CAT(0) 立方复形的大尺度维数。当这些界相互冲突时，我们便得到 G 可被余紧立方化的障碍。更强的是，这些障碍还阻止 G 成为粗中位数空间。作为应用，我们证明许多自由群-by-循环群不能被余紧立方化，即使在虚拟意义下也不行；并证明任何具有粗中位数的管状群都是虚拟紧特殊的。我们还构造了一个群，它是 CAT(0) 的、C(6) 的且虚拟特殊，却不与任何 CAT(0) 立方复形拟等距。这是首个不能被余紧立方化的 C(6) 群示例，解决了 Jankiewicz 的一个问题，并部分回答了 Wise 的一个问题。
英文摘要：
We provide geometric methods to give bounds on the large-scale dimension of CAT(0) cube complexes quasiisometric to a given group $G$. In situations where these bounds conflict we obtain obstructions to $G$ being cocompactly cubulated. More strongly, the obstructions prevent $G$ from being a coarse median space. As applications, we show that many free-by-cyclic groups cannot be cocompactly cubulated, even virtually, and prove that any tubular group with a coarse median is virtually compact special. We also exhibit a group that is CAT(0), $C(6)$, and virtually special, yet is not quasiisometric to any CAT(0) cube complex. This is the first example of a $C(6)$ group that cannot be cocompactly cubulated, resolving a question of Jankiewicz and partially answering a question of Wise.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
