Kravchenko A. Automorphisms of Kronrod-Reeb graphs of Morse functions on orientable compact surfaces

The dissertation is devoted to the study of discrete symmetries of smooth functions with isolated critical points on orientable compact surfaces. The paper focuses on groups of automorphisms of Kronrod-Reeb graphs of functions induced by diffeomorphisms, which preserving function and isotopic to the identity. The object of the study is smooth functions on compact surfaces with locally homogeneous singularities (in particular, Morse functions), as well as Kronrod-Reeb graphs of such functions. Theorems of realization of finite groups as groups of automorphisms of Kronrod-Reeb graphs for different classes of smooth functions (simple Morse functions, Morse functions of general position, arbitrary Morse functions, as well as functions with locally homogeneous singularities) on orientable compact surfaces are obtained. The methods of topology (general, algebraic, geometric, differential), as well as algebra and discrete mathematics are used in the work. The results of the dissertation are theoretical. They can be used in further research in topology, algebra, mathematical physics and other branches of since, whose methods are based on topological properties of smooth functions.