Soroka Y. Automorphisms of foliations on two-dimensional noncompact surfaces

The thesis is devoted to study of the homotopy types of automorphisms groups of nonsingular foliations on two-dimensional noncompact surfaces and automorphisms of singular foliations on the plane with a finite number of singular points. We describe an algebraic structure of the class of homeotopy groups of canonical foliations of rooted tree-like striped surfaces, and establish a connection between homeotopy groups of foliated homeomorphisms of canonical foliations on rooted tree-like striped surfaces and homeotopy groups their space of leaves. For an atlas of a striped surface we define a graph describing the information about gluing of the surface from strips and establish an isomorphism between the homeotopy group of the canonical foliation of that striped surface and the group of automorphisms of its graph. We also obtain necessary and sufficient conditions for foliated and topological equivalences of two pseudohharmonic functions of general position on the plane, whose level-sets form singular foliations with finite number of singularities and their space of leaves are Hausdorff.