On the first homology of automorphism groups of manifolds with geometric structures |
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Authors: | Kōjun Abe Kazuhiko Fukui |
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Affiliation: | (1) Department of Mathematical Sciences, Shinshu University, 390-8621 Matsumoto, Japan;(2) Department of Mathematics, Kyoto Sangyo University, 603-8555 Kyoto, Japan |
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Abstract: | 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. This research was partially supported by Grant-in-Aid for Scientific Research (No. 16540058), Japan Society for the Promotion of Science. This research was partially supported by Grant-in-Aid for Scientific Research (No. 14540093), Japan Society for the Promotion of Science. |
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Keywords: | Automorphism group first homology group G-manifold Foliated manifold |
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