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

In: Geometriae Dedicata, Vol. 134, No. 1, 2008, p. 197-202.

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

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Author

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

In: Geometriae Dedicata, Vol. 134, No. 1, 2008, p. 197-202.

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

Bibtex

@article{34db475250f84c9b9403543b143fd2a5,
title = "An index formula for the self-linking number of a space curve",
keywords = "writhe, total geodesic curvature, rotation index, winding number, self-linking number, Whitney degree, total torsion",
publisher = "Springer Netherlands",
author = "Peter Røgen",
year = "2008",
doi = "10.1007/s10711-008-9254-0",
volume = "134",
number = "1",
pages = "197--202",
journal = "Geometriae Dedicata",
issn = "0046-5755",

}

RIS

TY - JOUR

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

A1 - Røgen,Peter

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 -