Roll-spun knots
Roll-spun knots
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卷纺结
DOI：
10.1017/s0305004100075794
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发表时间：
1993
影响因子：
0.8
通讯作者：
M. Teragaito
中科院分区：
文献类型：
--
作者：
M. Teragaito
本文将研究由滚纺3球S3中的1节得到的4球S4中的2节。纺纱过程由Artin[2]介绍，并由Fox[7]和Zeeman[20]推广到捻纺。1960年，福克斯介绍了另一种纺纱工艺，称为滚纺纱。他只证明了捻纺八字形结不能得到滚纺八字形结。最后，Litherland[14]描述了变形纺丝的一般过程，并给出了滚锭纺丝的精确定义。我们注意到Fox的滚纺和Litherland的不一样：Fox的滚纺八字结是对称纺八字结，以[14]表示。
In this paper we will study 2-knots in the 4-sphere S4 which are obtained by roll-spinning 1-knots in the 3-sphere S3. The process of spinning was introduced by Artin[2] and generalized to twist-spinning by Fox [7] and Zeeman [20]. In [7] Fox introduced another variation of the spinning process, called roll-spinning. He only showed that the roll-spun figure-eight knot cannot be obtained by twist-spinning the figure-eight knot. Finally Litherland [14] described the general process of deform-spinning, and he gave a precise definition of roll-spinning. We remark that Fox's roll-spinning is not the same as Litherland's: Fox's roll-spun figure-eight knot is the symmetry-spun figure-eight knot in terms of [14].