Journal article
An index formula for the self-linking number of a space curve
Given an embedded closed space curve with non-vanishing curvature, its self-linking number is defined as the linking number between the original curve and a curve pushed slightly off in the direction of its principal normals. We present an index formula for the self-linking number in terms of the writhe of a knot diagram of the curve and either (1) an index associated with the tangent indicatrix and its antipodal curve, (2) two indices associated with a stereographic projection of the tangent indicatrix, or (3) the rotation index (Whitney degree) of a stereographic projection of the tangent indicatrix minus the rotation index of the knot diagram.
Language: | English |
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Publisher: | Springer Netherlands |
Year: | 2008 |
Pages: | 197-202 |
ISSN: | 15729168 and 00465755 |
Types: | Journal article |
DOI: | 10.1007/s10711-008-9254-0 |
ORCIDs: | Røgen, Peter |