关于立方配合物上局部椭圆作用的注记

arXiv: Group Theory Pub Date : 2018-10-16 DOI:10.2140/IIG.2020.18.1

Nils Leder, Olga Varghese

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引用次数: 7

摘要

我们从Sageev的结果推导出，当一个群在有限维CAT(0)立方复合体上以局部椭圆的方式作用时，它必须固定一个点。作为应用，我们给出了一个群G的例子，使得G不具有性质(T)，但G及其所有有限生成的子群不能在有限维CAT(0)立方复上没有不动点而作用，从而回答了Barnhill和Chatterji的问题。

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A note on locally elliptic actions on cube complexes

We deduce from Sageev's results that whenever a group acts locally elliptically on a finite dimensional CAT(0) cube complex, then it must fix a point. As an application, we give an example of a group G such that G does not have property (T), but G and all its finitely generated subgroups can not act without a fixed point on a finite dimensional CAT(0) cube complex, answering a question by Barnhill and Chatterji.

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arXiv: Group Theory

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