Whitney's index formula in higher dimensions and Laplace integrals

Details Whitney's index formula in higher dimensions and Laplace integrals Whitney's index formula in higher dimensions and Laplace integrals

1998-01-10

arxiv.org/abs/math/9801044v1

Mathematics

Differential Geometry

13 pages, LaTeX, no figures

Scientific paper

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).

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