论文标题
大脸部和加强的扇形引理
Large facing tuples and a strengthened sector lemma
论文作者
论文摘要
我们证明，在综合体为\ emph {hyperplane-extental-extental-extental}的其他假设下，我们证明了不可约，有限的，有限的，局部有限的，必不可少的CAT（0）立方体复合物的扇形引理；我们证明每个季度空间都包含一个半空间。为此，我们提供了有关触点图的LOXODORMIC异构体的已知结果的简化证明，避免使用圆盘图。 本文具有说明性元素。特别是，我们通过结合Ramsey的定理和Dilworth的定理来收集有关立方体复合物的结果。我们通过讨论Cubical组的山雀替代方案来说明这些技巧的使用，并提出了一些有关“量化”与等级 - 戒指和山雀替代方案相关的“量化”陈述的问题。
We prove a strengthened sector lemma for irreducible, finite-dimensional, locally finite, essential, cocompact CAT(0) cube complexes under the additional hypothesis that the complex is \emph{hyperplane-essential}; we prove that every quarterspace contains a halfspace. In aid of this, we present simplified proofs of known results about loxodromic isometries of the contact graph, avoiding the use of disc diagrams. This paper has an expository element; in particular, we collect results about cube complexes proved by combining Ramsey's theorem and Dilworth's theorem. We illustrate the use of these tricks with a discussion of the Tits alternative for cubical groups, and ask some questions about "quantifying" statements related to rank-rigidity and the Tits alternative.
