Whitney's index formula in higher dimensions and Laplace integrals
arXiv:math/9801044
Abstract
The famous Whitney formula relates the winding number of the smooth generic curve in the real plane to the number of its self-intersection points counted with appropriate signs. We extend this formula to smooth immersions of R^n to R^{2n}. Then use this result together with the general technique of Laplace integrals to get an explicit formula for the generator of the group H^n of Stiefel variety V(n,2n).
13 pages, LaTeX, no figures