Commutator Length of Leaf Preserving Diffeomorphisms

被引:1
作者
Fukui, Kazuhiko [1 ]
机构
[1] Kyoto Sangyo Univ, Dept Math, Kyoto 6038555, Japan
基金
日本学术振兴会;
关键词
commutator length; leaf preserving diffeomorphism; uniformly perfect;
D O I
10.2977/PRIMS/83
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We consider the group of leaf preserving C-infinity-diffeomorphisms for a C-infinity-foliation on a manifold which are isotopic to the identity through leaf preserving C-infinity-diffeomorphisms with compact support. We show that for a one-dimensional C-infinity-foliation F on the torus, this group is uniformly perfect if and only if F has no compact leaves. Moreover we consider the group of leaf preserving C-infinity-diffeomorphisms for the product foliation on S-1 x S-n which are isotopic to the identity through leaf preserving C-infinity-diffeomorphisms. Here the product foliation has leaves of the form {pt} x S-n. We show that this group is uniformly perfect for n >= 2.
引用
收藏
页码:615 / 622
页数:8
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