On the symmetry of composite ribbon knots
On the symmetry of composite ribbon knots
复制标题
复合带结的对称性
DOI：
10.1016/j.topol.2023.108417
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发表时间：
2023
影响因子：
0.6
通讯作者：
Toshifumi
中科院分区：
文献类型：
--
作者：
Tanaka;Toshifumi
结与其方向相反的镜像的连通和是丝带结。相反，我们证明，如果 K 0 和 K 1 是相对于色带一致性而言最小的结，并且 K 0 和 K 1 的连通和是色带一号结，则 K 0 相当于方向相反的 K 1 的镜像。我们还证明，两个环面结的连通和是切片结，那么它是环面结与其镜像的连通和。
The connected-sum of a knot and its mirror image with orientation reversed is a ribbon knot. Conversely, we show that if K 0 and K 1 are knots which are minimal with respect to ribbon concordance and the connected sum of K 0 and K 1 is a ribbon number one knot, then K 0 is equivalent to the mirror image of K 1 with orientation reversed. We also show that the connected sum of two torus knots is a slice knot, then it is a connected sum of a torus knot and its mirror image.