A reconstruction theorem for smooth foliated manifolds (Q649034)

The author shows that smooth foliated manifolds are determined by their automorphism groups by proving that every isomorphism between the groups of \(C^\infty\) automorphisms of two \(C^\infty\) foliated manifolds is induced by a diffeomorphism between the two manifolds that sends the leaves of one foliation onto the leaves of the other. This theorem is obtained by combining the technical results of this paper with a theorem of \textit{T. Rybicki} [Soochow J. Math. 22, No. 4, 525--542 (1996; Zbl 0869.58004)].