Whitney's index formula in higher dimensions and Laplace integrals
Yurii M. Burman
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 Rn to R2n. Then use this result together with the general technique of Laplace integrals to get an explicit formula for the generator of the group Hn of Stiefel variety V(n,2n).
Create a lesson
Related papers
Topological and spectral rigidity of hypersurface Zoll manifolds
Gustavo Martins
Stationary varifolds with singularities II
Camillo De Lellis, Jonas Hirsch, Zachary Lihn et al.
Alexandrov's Theorem for Integral Varifolds and Applications to Geometric Inequalities
Mitchell Gaudet
Deformations of harmonic maps with conical singularities
Dominik Gutwein, Thibault Langlais
The isoperimetric inequality and CMC hypersurfaces in Cartan-Hadamard manifolds
Shibing Chen, Mohammad Ghomi, Peng Wang
Finite-Time Singularities of the Kähler--Ricci Flow on Fano Bundles II
Wangjian Jian, Jian Song