Pryshlyak A. Topological properties of functions and vector fields on low-dimensional manifolds

Objects: functions, dynamical systems and 1-forms on low-dimensional manifolds. Goals: descriptions of topological properties of Morse-Smale fector fields and Morse functions on 3-manifolds, m-functions and m-fields, functions with isolated critical points on 2- and 3-manifolds, Whitney maps of surfaces to the plane. Methods: Morse theory, Smale theory of handle decompositions, low-dimensional topology. New theoretic results: It is given topological classifications of Morse-Smale vector fields and Morse functions on 3-manifolds, functions with isolated critical points on closed surfaces, functions with 3 and 4 critical points on 3-manifolds, m-functions and m-fields on 2= amd 3-manifolds, Whitney maps of surfaces to the plane; the theorems on indexes sum of a flow on a stratified set are proved. Employment: the results are important in the low-dimensional topology, in branch where functions and dynamical systems in low-dimensional are appeared.