Bondarenko A. Functions on 3-manifolds.

The classification of functions with four critical points from three-dimensional manifolds to the circle is considered, all possible Reeb graphs of such functions when the genus of the preimage of a regular point does not exceed 1 are constructed. A topological classification of maps from two-dimensional manifolds into the plane is obtained. The problem under consideration is the function from three-dimensional manifolds into the plane, the classification theorem of such functions is proved and some examples of calculations for projections with a fixed number of points of intersection and self-intersection are proposed.