Commutators of C∞-diffeomorphisms preserving a submanifold

Kōjun ABE; Kazuhiko FUKUI

doi:10.2969/jmsj/06120427

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Home > Journals > J. Math. Soc. Japan > Volume 61 > Issue 2 > Article

April, 2009 Commutators of

C^{\infty}

-diffeomorphisms preserving a submanifold

Kōjun ABE, Kazuhiko FUKUI

J. Math. Soc. Japan 61(2): 427-436 (April, 2009). DOI: 10.2969/jmsj/06120427

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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.

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Kōjun ABE. Kazuhiko FUKUI. "Commutators of $C^{\infty}$ -diffeomorphisms preserving a submanifold." J. Math. Soc. Japan 61 (2) 427 - 436, April, 2009. https://doi.org/10.2969/jmsj/06120427