On the first homology of automorphism groups of manifolds with geometric structures
On the first homology of automorphism groups of manifolds with geometric structures
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DOI：
10.2478/bf02475921
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发表时间：
2005-09
影响因子：
--
通讯作者：
K. Abe;K. Fukui
中科院分区：
文献类型：
--
作者：
K. Abe;K. Fukui
Hermann 和 Thurston 证明了具有光滑流形 M 的紧支持且与恒等式同位素的微分同胚群是完美群。我们考虑 M 具有几何结构的情况。在本文中，我们将调查微分同胚群的第一个同源性的最新结果，这些微分同胚群在 M 上保留平滑的 G 作用或叶状结构。我们也在 Lipschitz 类别中进行工作。
Hermann and Thurston proved that the group of diffeomorphisms with compact support of a smooth manifold M which are isotopic to the identity is a perfect group. We consider the case where M has a geometric structure. In this paper we shall survey on the recent results of the first homology of the diffeomorphism groups which preserve a smooth G-action or a foliated structure on M. We also work in Lipschitz category.