Geodesic
On the diffeomorphism groups of foliated manifolds
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 74-83

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In this paper, we introduce a certain topology on the group $\mathrm{Diff}_F(M)$ of all $C^r$-diffeomorphisms of the foliated manifold $(M;F)$, where $r\ge0$. This topology depends on the foliation and is called the $F$-compact-open topology. It coincides with the compact-open topology when $F$ is an $n$-dimensional foliation. If the codimension of the foliation is $n$, then the convergence in this topology coincides with the pointwise convergence, where $n=\dim M$. We prove that some subgroups of the group $\mathrm{Diff}_F(M)$ are topological groups with the $F$-compact-open topology. Throughout this paper, we use smoothness of the class $C^{\infty}$.
Keywords: manifold, topological group, compact-open topology.
Mots-clés : foliation 
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     author = {A. Ya. Narmanov and A. S. Sharipov},
     title = {On the diffeomorphism groups of foliated manifolds},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {74--83},
     publisher = {mathdoc},
     volume = {181},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_181_a9/}
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A. Ya. Narmanov; A. S. Sharipov. On the diffeomorphism groups of foliated manifolds. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Classical and Modern Geometry" Dedicated to the 100th Anniversary of the Birth of Professor Vyacheslav Timofeevich Bazylev. Moscow, April 22-25, 2019. Part 3, Tome 181 (2020), pp. 74-83. http://geodesic.mathdoc.fr/item/INTO_2020_181_a9/