# A. Ya. Narmanov

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Articles: 1

### On the group of foliation isometries

Methods Funct. Anal. Topology 15 (2009), no. 2, 195-200

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 $n=\operatorname{dim}M.$ It is proved that the group $G_F^{r}(M)$ is a topological group with compact-open topology, where $r\geq{0}.$ In addition it is showed some properties of F-compact-open topology.