Regular homotopy classes of singular maps
arXiv:math/0506566 · doi:10.1112/S0024611504015102
Abstract
Two locally generic maps f,g : M^n --> R^{2n-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 M^n is a closed n-manifold then the regular homotopy class of every locally generic map f : M^n --> R^{2n-1} is completely determined by the number of its singular points provided that f is singular (i.e., f is not an immersion).
23 pages, 3 figures