Homotopy type of stabilizers of smooth functions with non-isolated singularities on surfaces

The paper is devoted to the study of homotopy properties of stabilizers of smooth functions on oriented surfaces, i.e., groups of diffeomorphisms of surfaces preserving a given function. For some class of smooth functions which is a generalization of the class of Morse-Bott functions on oriented surfaces, the homotopy type of the connected component of the identity map of the stabilizer is completely described.