Diffeomorphisms Of Foliated Manifolds

Abstract

The set Diff(M) of all diffeomorphisms of a manifold M onto itself is the group related to composition and inverse mapping. The group of diffeomorphisms of smooth manifolds is of great importance in differential geometry and in analysis. It is known that the group Diff(M) is a topological group in compact open topology. In this paper we investigate the group DiffF(M) of diffeomorphisms foliated manifold (M, F) with foliated compact open topology. It is proven that foliated compact open topology of the group DiffF(M) has a countable base. It is also proven that the group DiffF(M) is a topological group with foliated compact open topology. Also some one-parameter subgroups of the group DiffF(M) are found and studied for the foliations generated by special submersions.