Whitney's formulas for curves on surfaces
arXiv:0911.0393 · doi:10.1007/s10711-010-9521-8
Abstract
The classical Whitney formula relates the number of times an oriented plane curve cuts itself to its rotation number and the index of a base point. In this paper we generalize Whitney's formula to curves on an oriented punctured surface. To define analogs of the rotation number and the index of a base point of a curve, we fix an arbitrary vector field on the surface. Similar formulas are obtained for non-based curves.
Published version; 10 pages, 6 figures