On the Group of Foliation Isometries

Abstract

The purpose of our paper is to introduce some topology on the group GrF(M) of all Cr-isometries of foliated manifold (M, F), which depends on a foliation F and coincides with compact-open topology when F is an n-dimensional foliation. If the codimension of F is equal to n, convergence in our topology coincides with pointwise convergence, where n = dimM. It is proved that the group GrF(M) is a topological group with compact-open topology, where r ≥ 0. In addition it is showed some properties of F-compact-open topology.