一些无穷图的小消去标记及其应用

IF 4.9 1区 数学 Q1 MATHEMATICS
Damian Osajda
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引用次数: 93

摘要

对有限次有限图的无限序列构造了小消去标记。我们用它们来定义群的无限图形化的小消去表示。这种技术允许我们提供具有奇异性质的群的例子:-我们构造了第一个有限生成的粗不可服从群(即没有Guoliang Yu的性质A的群)的例子,这些群可以粗嵌入到Hilbert空间中。此外,我们的基团可以很好地作用于CAT(0)立方配合物。-我们构造了有限生成群的第一个例子,扩展器等距嵌入到他们的Cayley图中-相反,在Gromov怪物的情况下,扩展器甚至没有粗略嵌入。我们提出了进一步的应用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Small cancellation labellings of some infinite graphs and applications
We construct small cancellation labellings for some infinite sequences of finite graphs of bounded degree. We use them to define infinite graphical small cancellation presentations of groups. This technique allows us to provide examples of groups with exotic properties: - We construct the first examples of finitely generated coarsely non-amenable groups (that is, groups without Guoliang Yu's Property A) that are coarsely embeddable into a Hilbert space. Moreover, our groups act properly on CAT(0) cubical complexes. - We construct the first examples of finitely generated groups, with expanders embedded isometrically into their Cayley graphs - in contrast,in the case of the Gromov monster expanders are not even coarsely embedded. We present further applications.
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来源期刊
Acta Mathematica
Acta Mathematica 数学-数学
CiteScore
6.00
自引率
2.70%
发文量
6
审稿时长
>12 weeks
期刊介绍: Publishes original research papers of the highest quality in all fields of mathematics.
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