Feshchenko B. Deformations of smooth functions on 2-torus

The thesis is devoted to study homotopy properties of smooth functions on surfaces. In this thesis we studied orbits of smooth functions on a 2-torus with respect to the actions of groups of diffeomorphisms. We give a complete description of the fundamental groups of orbits smooth of functions on 2-torus for a large class of smooth functions, which contains the set of Morse functions that is everywhere dense in the space of all smooth functions. We also consider actions of finite groups on surfaces that preserve some special partition of surfaces. Sufficient conditions under which these actions are induced by some actions of this group by diffeomorphisms which preserve the specified smooth function have established.