Whitney's formulas for curves on surfaces

Yurii Burman; Michael Polyak

doi:10.1007/s10711-010-9521-8

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arXiv · 0911.0393

Whitney's formulas for curves on surfaces

Yurii Burman·Michael Polyak

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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.

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BibTeX RIS

Yurii Burman, Michael Polyak. 2009-11-02. Whitney's formulas for curves on surfaces. https://doi.org/10.1007/s10711-010-9521-8

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