对合Khovanov同调与等变纽结II
Involutive Khovanov homology and equivariant knots II
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中文总结 AI 辅助
本文将对合Khovanov同调框架推广到对合缠结，实现了相关同调与不变量的分治加速计算，并得到存在奇异切片圆盘对的强可逆纽结新例子。
中文摘要 AI 辅助
受Bar-Natan构造缠结Khovanov同调的思路启发，我们将对合Khovanov同调的框架推广到对合缠结上，这使得对合Khovanov同调和等变Rasmussen不变量可采用分治计算，大幅提升了算法计算速度。借助该方法，我们得到了强可逆纽结的新例子，这类纽结的切片圆盘无法相对于边界光滑同痕于其对称对应物，具体而言，我们证明了pretzel纽结P(-3,3,-3)和P(-5,5,-5)的Whitehead双缠结存在奇异切片圆盘对。
英文摘要
In the spirit of Bar-Natan's formulation of Khovanov homology for tangles, we extend the framework of involutive Khovanov homology to involutive tangles. This enables a divide-and-conquer computation of involutive Khovanov homology and the equivariant Rasmussen invariant, which results in a significant speedup for the algorithmic computation. With this, we obtain new examples of strongly invertible knots for which no slice disk is smoothly isotopic rel boundary to its symmetric counterpart. In particular, we show that the Whitehead doubles of the pretzel knots $P(-3, 3, -3)$ and $P(-5, 5, -5)$ admit exotic pairs of slice disks.
