On the structure of the group of Lipschitz homeomorphisms and its subgroups
On the structure of the group of Lipschitz homeomorphisms and its subgroups
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关于Lipschitz同胚群及其子群的结构
DOI：
10.2969/jmsj/05330501
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
K. Fukui
中科院分区：
文献类型：
--
作者：
K. Abe;K. Fukui
我们考虑Lipschitz流形及其子群的Lipschitz同胚群。首先，我们研究了Lipschitz同胚群的性质，证明了Lipschitz同胚群的局部可缩性和完备性。其次，利用这一结果，我们证明了当G是紧李群时，闭Lipschitz流形上的主G-丛的等变Lipschitz同胚群的单位分支是完美的。
We consider the group of Lipschitz homeomorphisms of a Lipschitz manifold and its subgroups. First we study properties of Lipschitz homeomorphisms and show the local contractibility and the perfectness of the group of Lipschitz homeomorphisms. Next using this result we can prove that the identity component of the group of equivariant Lipschitz homeomorphisms of a principal G-bundle over a closed Lipschitz manifold is perfect when G is a compact Lie group.