Open Access
VOL. 1 | 2000 On the Structure of Automorphisms of Manifolds
Kojun Abe, Kazuhiko Fukui

Editor(s) Ivaïlo M. Mladenov, Gregory L. Naber

Geom. Integrability & Quantization, 2000: 7-16 (2000) DOI: 10.7546/giq-1-2000-7-16


Thurston [16] proved that the group Diff$^{\infty}(M)$ of a smooth manifold $M$ is perfect, which implies the first homology group is trivial. If $M$ has a geometric structure, then the first homology of the group of automorphisms of $M$ preserving the geometric structure is not necessarily trivial. There are many results concerning this field. In this paper, we shall summarize the results of the first homology groups of automorphisms of manifolds with geometric structure.


Published: 1 January 2000
First available in Project Euclid: 5 June 2015

zbMATH: 0978.58003
MathSciNet: MR2152474

Digital Object Identifier: 10.7546/giq-1-2000-7-16

Rights: Copyright © 2000 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


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