Whitney's formulas for curves on surfaces
Geometric Topology
2019-02-06 v2
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.
Cite
@article{arxiv.0911.0393,
title = {Whitney's formulas for curves on surfaces},
author = {Yurii Burman and Michael Polyak},
journal= {arXiv preprint arXiv:0911.0393},
year = {2019}
}
Comments
Published version; 10 pages, 6 figures