Whitney's formulas for curves on surfaces

Details Whitney's formulas for curves on surfaces Whitney's formulas for curves on surfaces

2009-11-02

arxiv.org/abs/0911.0393v1

Geometriae Dedicata 151 (2011), 97--106

Mathematics

Geometric Topology

9 pages, 5 figures

Scientific paper

10.1007/s10711-010-9521-8

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.

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