Commutators of C∞-diffeomorphisms preserving a submanifold

Commutators of C∞-diffeomorphisms preserving a submanifold

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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Veröffentlicht in:Journal of the Mathematical Society of Japan 2009-04, Vol.61 (2), p.427-436
Hauptverfasser: ABE, Kōjun, FUKUI, Kazuhiko
Format: Artikel
Sprache:eng
Schlagworte:
57R50
58D05
commutator subgroup
compact manifold with boundary
diffeomorphism group
uniformly perfect
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Zusammenfassung: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.
ISSN:0025-5645
1881-2333
DOI:10.2969/jmsj/06120427