## Proceedings of the International Conference on Geometry, Integrability and Quantization

### On the Structure of Automorphisms of Manifolds

#### Abstract

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.

#### Article information

Dates
First available in Project Euclid: 5 June 2015

https://projecteuclid.org/ euclid.pgiq/1433524874

Digital Object Identifier
doi:10.7546/giq-3-2002-11-63

Mathematical Reviews number (MathSciNet)
MR2152474

Zentralblatt MATH identifier
0978.58003

#### Citation

Abe, Kojun; Fukui, Kazuhiko. On the Structure of Automorphisms of Manifolds. Proceedings of the International Conference on Geometry, Integrability and Quantization, 7--16, Coral Press Scientific Publishing, Sofia, Bulgaria, 2000. doi:10.7546/giq-3-2002-11-63. https://projecteuclid.org/euclid.pgiq/1433524874