Proper Actions and a Compactness Condition 1
Proper Actions and a Compactness Condition 1
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正确的行动和紧凑条件 1
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
R. Lipsman
中科院分区：
文献类型：
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作者：
R. Lipsman
设X = G=H是齐性空间，G是连通李群，H是闭连通子群。如果G是一个离散子群，那么已经研究过的几个经典问题是：刻画nX何时是流形;何时是紧致流形;以及，在这两种情况下，描述的结构含义。如果G是代数的，则可以用它的Zagliki闭包L =来代替，并考虑关于L的类似问题。在一篇基础论文[4]中，小林正是这样做的，他发现了这两组问题之间的强烈相似之处。然后，他开始对后者进行深入的调查。他首先指出nX是流形的标准准则|即i既适当地不连续又自由地作用在X上。然后，他开发了L的这些性质的连续类似物，|其中一个很有名另一个不太有名我们在这里陈述这些属性。闭（连通）子群LG在X = G=H上的作用称为
Suppose X = G=H is a homogeneous space, with G a connected Lie group and H a closed connected subgroup. If G is a discrete subgroup, then several classical problems that have been studied are : to characterize when nX is a manifold; when it is a compact manifold; and, in either of these situations, to delineate the structural implications for . If G is algebraic, one can replace by its Zariski-closure L = and consider analogous problems concerning L. In a basic paper [4], Kobayashi has done exactly that and he has discovered strong parallels between the two sets of problems. He then initiates an intense investigation of the latter set. He begins by noting the standard criteria for nX to be a manifold|namely i acts both properly discontinuous and freely on X . He then develops continuous analogs of these properties for L|one of them well-known, another less so. We state these properties here. The action of a closed (connected) subgroup L G on X = G=H is said to be