Spaces with measured walls, the Haagerup property and property (T)
Spaces with measured walls, the Haagerup property and property (T)
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DOI：
10.1017/s0143385704000185
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发表时间：
2004-10
影响因子：
0.9
通讯作者：
P. Cherix;Florian Martin;A. Valette
中科院分区：
文献类型：
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作者：
P. Cherix;Florian Martin;A. Valette
我们引入了带有可测量墙壁的空间的概念，推广了Haglund和Paulin （simplicit<e:1> de groups d’automorphismes d’spaces）提出的带有墙壁的空间的概念。几何学。托波尔。专著1(1998),181-248)。我们观察到，如果一个局部紧群G恰当地作用于具有测量壁的空间，则G具有哈格鲁普性质。我们推测这个逆命题成立，并证明了以下几类群：具有Haagerup性质的离散群、SO（n, 1）的闭子群、作用于实树的群、K为全局域的SL2(K)和可服从群。
We introduce the notion of a space with measured walls, generalizing the concept of a space with walls due to Haglund and Paulin (Simplicité de groupes d'automorphismes d'espaces à courbure négative. Geom. Topol. Monograph1 (1998), 181–248). We observe that if a locally compact group G acts properly on a space with measured walls, then G has the Haagerup property. We conjecture that the converse holds and we prove this conjecture for the following classes of groups: discrete groups with the Haagerup property, closed subgroups of SO(n, 1), groups acting properly on real trees, SL2(K) where K is a global field and amenable groups.