JP Journal of Geometry and Topology
Volume 2, Issue 3, Pages 203 - 221
(November 2002)
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A COMBINATORIAL RELATION BETWEEN WINDING NUMBERS OF CLOSED CURVES IN A PLANE
Mitsunori Imaoka (Japan) and Isao Takata (Japan)
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Abstract:
We have two types of the winding numbers of a smooth closed curve in a plane. The first one is defined as the degree of the Gauss map associated with the unit tangent vectors over the closed curve, and the second one is the so-called looping number defined to be the number of times that the closed curve goes round a given point not on the closed curve. We can regard the former as the global winding number and the latter as the local winding number, and generalize those notions for the union of a finite number of closed curves. In this paper, we show a combinatorial relation between such two types of winding numbers using what we call the weights of the intersection points. |
| Keywords and phrases: winding numbers, Whitney numbers, Gauss maps. |
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