On the group of foliation isometries - Sharipov, A. S.; Narmanov, A. Ya. (Methods of Functional Analysis and Topology, 2009)
The purpose of our paper is to introduce some topology on the group G_F^r(M) of all C^r-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 G_F^r(M) is a topological group with compact-open topology, where r≥0. In addition it is showed some properties of F-compact-open topology.