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In knot theory, there are several competing notions of the quantity ''writhe'', or ''Wr''. In one sense, it is purely a property of an oriented link diagram and assumes integer values. In another sense, it is a quantity that describes the amount of "coiling" of a mathematical knot (or any closed, simple curve) in three-dimensional space and assumes real numbers as values. In both cases, ''writhe'' is a geometric quantity, meaning that while deforming a curve (or diagram) in such a way that does not change its topology, one may still change its ''writhe''.〔 ==Writhe of link diagrams== In knot theory, the ''writhe'' is a property of an oriented link diagram. The writhe is the total number of ''positive crossings'' minus the total number of ''negative crossings''. A direction is assigned to the link at a point in each component and this direction is followed all the way around each component. If as you travel along a link component and cross over a crossing, the strand underneath goes from right to left, the crossing is positive; if the lower strand goes from left to right, the crossing is negative. One way of remembering this is to use a variation of the right-hand rule. For a knot diagram, using the right-hand rule with either orientation gives the same result, so the writhe is well-defined on unoriented knot diagrams. The writhe of a knot is unaffected by two of the three Reidemeister moves: moves of Type II and Type III do not affect the writhe. Reidemeister move Type I, however, increases or decreases the writhe by 1. This implies that the writhe of a knot is ''not'' an isotopy invariant of the knot itself — only the diagram. By a series of Type I moves one can set the writhe of a diagram for a given knot to be any integer at all. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Writhe」の詳細全文を読む スポンサード リンク
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