Journal of the Mathematical Society of Japan

Commutators of C-diffeomorphisms preserving a submanifold

Kōjun ABE and Kazuhiko FUKUI

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We consider the group of C-diffeomorphisms of M which is isotopic to the identity through C-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

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

First available in Project Euclid: 13 May 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R50: Diffeomorphisms
Secondary: 58D05: Groups of diffeomorphisms and homeomorphisms as manifolds [See also 22E65, 57S05]

diffeomorphism group commutator subgroup compact manifold with boundary uniformly perfect


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.

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