Khokhliuk O. Homotopy types of spaces of differentiable mappings

The thesis is devoted to the study of the homotopy types of different classes of smooth mappings between manifolds. In particular, we study groups of diffeomorphisms of foliations with singularities of Morse-Bott type, as well as open subsets in the spaces of differentiable mappings of different smoothness between smooth manifolds. The objects of study are smooth manifolds, groups of diffeomorphisms of foliations, Whitney topologies, Morse-Bott functions. It is proved that for a Morse-Bott foliation the restriction map from the group of leaf-preserving diffeomorphisms of this foliation to the group of diffeomorphisms of the union of singular leaves is a locally trivial fibration. A result about weak homotopy equivalence of spaces of different classes of smoothness of mappings between manifolds is established. A result of the dissertation is theoretical.