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Статья

Whitney's formulas for curves on surfaces

Geometriae Dedicata. 2011. Vol. 151. No. 1. P. 97-106.
Burman Y. M., Polyak M.

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 m;n, obtaining a family of identities indexed by elements of 1(m;n). To de ne analogs of the rotation number and the index of a base point of a curve , we x an arbitrary vector eld on m;n. Similar formulas are obtained for non-based curves.