论文标题
分裂链接的化妆品交叉猜想
The cosmetic crossing conjecture for split links
论文作者
论文摘要
考虑到沿着非平凡频段的拆分两组分链路的频带总和，我们通过向频段添加任意数量的完整曲折来获得由整数索引的结系列。我们表明，这个家庭中的结具有相同的Heegaard打结同源性和相同的Instanton打结浮子同源性。相比之下，化妆品交叉猜想的概括预测，这个家族的结都是不同的。我们通过表明这个家庭中的任何两个结具有独特的Khovanov同源性来验证这一预测。一路上，我们证明了三个结同源物中的每一个都检测到了琐碎的频段。
Given a band sum of a split two-component link along a nontrivial band, we obtain a family of knots indexed by the integers by adding any number of full twists to the band. We show that the knots in this family have the same Heegaard knot Floer homology and the same instanton knot Floer homology. In contrast, a generalization of the cosmetic crossing conjecture predicts that the knots in this family are all distinct. We verify this prediction by showing that any two knots in this family have distinct Khovanov homology. Along the way, we prove that each of the three knot homologies detects the trivial band.
