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Self-linking number
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Self-linking number : ウィキペディア英語版
Self-linking number
In knot theory, the self-linking number is an invariant of framed knots. It is related to the linking number of curves.
A framing of a knot is a choice of a non-tangent vector at each point of the knot. Given a framed knot ''C'', the self-linking number is defined to be the linking number of ''C'' with a new curve obtained by pushing points of ''C'' along the framing vectors.
Given a Seifert surface for a knot, the associated Seifert framing is obtained by taking a tangent vector to the surface pointing inwards and perpendicular to the knot. The self-linking number obtained from a Seifert framing is always zero.
The blackboard framing of a knot is the framing where each of the vectors points in the vertical (''z'') direction. The self-linking number obtained from the blackboard framing is called the Kauffman self-linking number of the knot. This is not a knot invariant because it is only well-defined up to regular isotopy.
==References==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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