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achiral knot

无手征纽结

本站译名 几何拓扑与低维拓扑 义项编号TS-2197

英文别名
amphicheiral knot;acheiral knot
中文别名
双手征纽结

外文出处

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Symplectic Geometry 封面

《Symplectic Geometry》 · 第 15 页 · Section 1.7,Topological symmetries(纽结相等按环境同痕解释)

Let \(r:\mathbb R^3\longrightarrow\mathbb R^3\) be the map \((x,y,z)\longmapsto(-x,-y,-z)\); this is called central inversion or reflection in the origin. The image \(r(K)\) of a knot \(K\) is called the mirror image, reflection, or obverse of \(K\) and is denoted by \(K^*\). […] If \(K\) and its mirror image are different then we say that \(K\) is cheiral (handed) and it occurs in a left-handed (laevo) and a right-handed (dextro) form. If \(K=K^*\) then we say that \(K\) is acheiral or amphicheiral. The reflection of \(K\) is independent of the choice of \(r\): the image of \(K\) under any other orientation-reversing homeomorphism will be ambient isotopic to \(r(K)\).

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