Functions with isolated singularities on surfaces

الأصل · EN

Let M be a smooth connected compact surface, P be either the real line R¹ or the circle S¹, and f:M-->P be a smooth mapping. In a previous series of papers for the case when f is a Morse map the author calculated the homotopy types of stabilizers and orbits of f with respect to the right action of the diffeomorphisms group of M. The present paper extends those calculations to a large class of maps M-->P with degenerate singularities satisfying certain set of axioms.