THE TURNED TORUS KNOT IN S4
THE TURNED TORUS KNOT IN S4
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S4 中的转向圆环结
DOI：
10.1142/s0218216593000155
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发表时间：
1993
影响因子：
0.5
通讯作者：
J. Boyle
中科院分区：
文献类型：
--
作者：
J. Boyle
四元球面中的旋转纽结环面是由纽结曲线沿着圆刚性扫掠形成的。或者，当打结曲线沿着圆扫掠时，我们可以给它一个完整的圈数（Dehn扭曲）。我们表明，由此产生的纽结环面只取决于纽结曲线和是否圈数是偶数或奇数。偶数和奇数的旋转环面有非纯补。在某些情况下，这被推广到包括扭转旋转的环面结。
A spun knotted torus in the 4-sphere is formed by rigidly sweeping a knotted curve along a circle. Alternately, as the knotted curve is swept along the circle we could give it a number of full turns (Dehn twists). We show the resulting knotted torus depends only on the knotted curve and whether the number of turns is even or odd. The even and odd turned spun tori have nondiffeomorphic complements. This is generalized in some cases to include twist spun turned torus knots.