Convergence groups and configuration spaces
Convergence groups and configuration spaces
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DOI：
10.1515/9783110806861.23
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
B. Bowditch
中科院分区：
文献类型：
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作者：
B. Bowditch
我们给一个帐户的收敛群体的角度来看，适当的行为不连续的空间不同的三元组。我们给出了一个证明的等价性，这个特征与动力学定义的Gehring和马丁。我们把注意力集中在一致收敛群上，即那些在不同三元组空间上的作用也是余紧的，并从纯粹动力学的角度探讨它们的一些性质。我们表明，在任何连续空间中的不同的无序n元组的空间是连接的。此外，除了圆或弧之外的任何可度量连续统中的不同有序n元组的空间也是连通的。
We give an account of convergence groups from the point of view of groups which act properly discontinuously on spaces of distinct triples. We give a proof of the equivalence of this characterisation with the dynamical definition of Gehring and Martin. We focus our attention on uniform convergence groups, i.e. those for which the action on the space of distinct triples is also cocompact, and explore some of their properties from a purely dynamical point of view. We show that the space of distinct unordered n-tuples in any continuum is connected. Moreover, the spaces of distinct ordered n-tuples in any metrisable continuum other than a circle or an arc is also connected.