An index formula for the self-linking number of a space curve

Publication: Research - peer-reviewJournal article – Annual report year: 2008

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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.
Original languageEnglish
JournalGeometriae Dedicata
Publication date2008
Volume134
Issue1
Pages197-202
ISSN0046-5755
DOIs
StatePublished
CitationsWeb of Science® Times Cited: 1

Keywords

  • writhe, total geodesic curvature, rotation index, winding number, self-linking number, Whitney degree, total torsion
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