2009/11/30 by Yurii Burman, Michael Polyak
Mathematics · #math.GT #msc:57N35 #msc:57R42 #msc:57M20
paper · pdf · doi:10.1007/s10711-010-9521-8
published as Geometriae Dedicata 151 (2011), 97--106 · Published version; 10 pages, 6 figures
arxiv created 2019/02/05 · arxiv updated 2019/02/06
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.