## Journal of the Mathematical Society of Japan

### Commutators of $C^{\infty}$-diffeomorphisms preserving a submanifold

#### Abstract

We consider the group of $C^{\infty}$-diffeomorphisms of $M$ which is isotopic to the identity through $C^{\infty}$-diffeomorphisms preserving $N$ for a compact manifold pair $(M,N)$ and prove that the group is perfect. Also we prove that it is uniformly perfect for a certain compact manifold with boundary.

#### Article information

Source
J. Math. Soc. Japan, Volume 61, Number 2 (2009), 427-436.

Dates
First available in Project Euclid: 13 May 2009

https://projecteuclid.org/euclid.jmsj/1242220717

Digital Object Identifier
doi:10.2969/jmsj/06120427

Mathematical Reviews number (MathSciNet)
MR2532896

Zentralblatt MATH identifier
1169.57029

#### Citation

ABE, Kōjun; FUKUI, Kazuhiko. Commutators of $C^{\infty}$ -diffeomorphisms preserving a submanifold. J. Math. Soc. Japan 61 (2009), no. 2, 427--436. doi:10.2969/jmsj/06120427. https://projecteuclid.org/euclid.jmsj/1242220717

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