Cosmetic two‐strand twists on fibered knots
Cosmetic two‐strand twists on fibered knots
复制标题
纤维结上的化妆品两股捻线
DOI：
10.1112/topo.12164
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发表时间：
2020
影响因子：
1.1
通讯作者：
C. Rogers
中科院分区：
文献类型：
--
作者：
C. Rogers
设K是有理同调球M中的一个结。本文研究了当在两条相反方向的链上加入m b> 0个半扭转而保持K的其余部分不变时，K会产生一个结同位素的问题。当m为偶数时，这种m阶的双股扭曲是一种广义交叉变化，当m=±1时，是一种非相干带手术。K上的一种装饰性的双股扭曲是一种产生同位素结的非功能性扭曲。我们证明M中的纤维结不允许表面的广义交叉变化。进一步，我们证明了如果K是纤维的，那么只有当m=±1时，由纤维表面上的分离弧决定的奇数阶m的两股捻度才能是美观的。
Let K be a knot in a rational homology sphere M . This paper investigates the question of when modifying K by adding m>0 half‐twists to two oppositely oriented strands, while keeping the rest of K fixed, produces a knot isotopic to K . Such a two‐strand twist of order m , as we define it, is a generalized crossing change when m is even and a non‐coherent band surgery when m=±1 . A cosmetic two‐strand twist on K is a non‐nugatory one that produces an isotopic knot. We prove that fibered knots in M admit no cosmetic generalized crossing changes. Further, we show that if K is fibered, then a two‐strand twist of odd order m that is determined by a separating arc in a fiber surface for K can only be cosmetic if m=±1 .