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

Publication: Research - peer-review › Journal article – Annual report year: 2008

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**An index formula for the self-linking number of a space curve.** / Røgen, Peter.

Publication: Research - peer-review › Journal article – Annual report year: 2008

### Harvard

*Geometriae Dedicata*, vol 134, no. 1, pp. 197-202., 10.1007/s10711-008-9254-0

### APA

*Geometriae Dedicata*,

*134*(1), 197-202. 10.1007/s10711-008-9254-0

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### MLA

*Geometriae Dedicata*. 2008, 134(1). 197-202. Available: 10.1007/s10711-008-9254-0

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### Bibtex

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### RIS

TY - JOUR

T1 - An index formula for the self-linking number of a space curve

AU - Røgen,Peter

PB - Springer Netherlands

PY - 2008

Y1 - 2008

N2 - 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.

AB - 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.

KW - writhe

KW - total geodesic curvature

KW - rotation index

KW - winding number

KW - self-linking number

KW - Whitney degree

KW - total torsion

U2 - 10.1007/s10711-008-9254-0

DO - 10.1007/s10711-008-9254-0

JO - Geometriae Dedicata

JF - Geometriae Dedicata

SN - 0046-5755

IS - 1

VL - 134

SP - 197

EP - 202

ER -