On the Perfectness of Nontransitive Groups of Diffeomorphisms

Abstract

. It is proven that the identity component of the group preserving the leaves of a generalized foliation is perfect. This shows that a well-known simplicity theorem on the diffeomorphism group extends to the nontransitive case. 1. Introduction The goal of this paper is to show a perfectness theorem for a class of diffeomorphism groups connected with foliations. Throughout by foliations we shall understand generalized foliations in the sense of P.Stefan [12]. Given a smooth foliation F on a manifold M , the symbol Diff(T n ; F) 0 stands for the identity component of the group of all leaf preserving C 1 -smooth diffeomorphisms of (M;F) with compact support. Theorem 1.1. Let F be a foliation on M with no leaves of dimension 0. Then the group Diff(T n ; F) 0 and its universal covering Diff(T n ; F) 0 are perfect. Theorem 1.1 and its proof extend a well known theorem of W.P.Thurston [15] stating that Diff(M) 0 , the identity component of the group of all compactly supported dif..

Similar works

This paper was published in CiteSeerX.

Having an issue?

Is data on this page outdated, violates copyrights or anything else? Report the problem now and we will take corresponding actions after reviewing your request.