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.
@article{bwmeta1.element.doi-10_2478_BF02475921,
author = {K\=ojun Abe and Kazuhiko Fukui},
title = {On the first homology of automorphism groups of manifolds with geometric structures},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {516-528},
zbl = {1117.57032},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475921}
}
Kōjun Abe; Kazuhiko Fukui. On the first homology of automorphism groups of manifolds with geometric structures. Open Mathematics, Tome 3 (2005) pp. 516-528. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475921/
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