论文标题
通过无效的曲折和多扭手取消打结
Unknotting via null-homologous twists and multi-twists
论文作者
论文摘要
打结k的数量是将K转换为UNNENGOT所需的无原样曲折的最小数量。这样的扭曲可以看作是交叉变化的概括，因为经典的交叉变化可以通过2条链的无原样扭曲来实现。虽然未打结的数字在光滑的4摄氏度上具有上限，但无弯曲的数字在拓扑4代上给出了上限。手术描述编号允许单个扭曲区域中多个无效的曲折算作一个操作，位于拓扑4生成和无差数之间。我们表明，无限多个结的不一致和手术描述数字不同，尽管我们还发现无扭曲的数字最多是手术描述编号加1的两倍。
The untwisting number of a knot K is the minimum number of null-homologous twists required to convert K to the unknot. Such a twist can be viewed as a generalization of a crossing change, since a classical crossing change can be effected by a null-homologous twist on 2 strands. While the unknotting number gives an upper bound on the smooth 4-genus, the untwisting number gives an upper bound on the topological 4-genus. The surgery description number, which allows multiple null-homologous twists in a single twisting region to count as one operation, lies between the topological 4-genus and the untwisting number. We show that the untwisting and surgery description numbers are different for infinitely many knots, though we also find that the untwisting number is at most twice the surgery description number plus 1.
