Budnytska N. Topological properties of closed 1-forms on surfaces.

This thesis is devoted to the study of topological properties of closed 1-forms. The topological classifications of closed 1-forms with arbitrary integral curves on closed surfaces and surfaces with boundary are obtained. Possible type of the integral curves of closed 1-forms are established. The theorems for dividing closed surfaces by the integral curves of closed 1-forms to domains that filled by the same curves are proved. The conditions under which arbitrary curves defined on closed surfaces are the integral curves of a closed 1-form are finded. The necessary and sufficient conditions under which the graph included in surface is the graph of closed 1-form are established. The number of topological nonequivalent closed 1-forms with closed recurrent curves on orientable surfaces of genus 0, 1 and noclosed recurrent curves on the orientable surface of genus 1 are estimated.