Viatchaninova O. Functions on a three-dimensional manifold with a boundary

The dissertation is devoted to the study of the topological classification of functions without critical points on a three-dimensional body whose restriction to the boundary has one maximum, one minimum. Generalize the concept of atoms and molecules to functions without internal critical points on the three-dimensional body, and a finite number of critical points of the restriction of the border. The resulting formula change and components depending on the level of the index point. The question of what kind of simple functions on the polar surfaces can be extended to functions without critical points on a three-dimensional body at a certain embedding of the surface in three-dimensional space. Homotopy equivalence criterion proved without internal critical points on the three-dimensional solids. On its basis the classification obtained homotopy m-dimensional functions on the disk and torus.