An index formula for the self-linking number of a space curve
- 88 Downloads
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.
KeywordsSelf-linking number Writhe Winding number Rotation index Whitney degree Total torsion Total geodesic curvature
Mathematics Subject Classification (2000)57M25
Unable to display preview. Download preview PDF.