Commutators of C∞-diffeomorphisms preserving a submanifold

Kōjun ABE; Kazuhiko FUKUI

doi:10.2969/jmsj/06120427

Journal of the Mathematical Society of Japan

Online ISSN : 1881-1167
Print ISSN : 0025-5645
ISSN-L : 0025-5645

Commutators of C^∞-diffeomorphisms preserving a submanifold

Kōjun ABE, Kazuhiko FUKUI

著者情報

キーワード: diffeomorphism group, commutator subgroup, compact manifold with boundary, uniformly perfect

ジャーナルフリー

2009 年 61 巻 2 号 p. 427-436

DOI https://doi.org/10.2969/jmsj/06120427

詳細

抄録

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.