Regular homotopy classes of singular maps

الأصل · EN

Two locally generic maps f,g: Mⁿ --> R²ⁿ⁻¹ are regularly homotopic if they lie in the same path-component of the space of locally generic maps. Our main result is that if n is not 3 and Mⁿ is a closed n-manifold then the regular homotopy class of every locally generic map f: Mⁿ --> R²ⁿ⁻¹ is completely determined by the number of its singular points provided that f is singular (i.e., f is not an immersion).