由Lee类的可除性得到的一族切片环面不变量
A family of slice-torus invariants from the divisibility of Lee classes
AI总结：
本文从Lee类的可除性构造了一族切片环面不变量，在特定参数下与Rasmussen不变量一致，并发现一个非切片环面的未约化不变量，表明其与约化不变量线性无关。
摘要：
我们给出了一族切片环面不变量$\tilde{ss}_c$，每个不变量由约化Khovanov同调的一个变体中约化Lee类的$c$-可除性定义，并以任意主理想整环$R$中的素元$c$为参数。对于特殊情况$(R,c)=(F[H],H)$，其中$F$为任意域，我们证明$\tilde{ss}_c$与$F$上的Rasmussen不变量$s^F$一致。与第一作者在先前论文中定义的未约化不变量$ss_c$相比，我们证明对于$(R,c)=(F[H],H)$和$(\mathbb{Z},2)$，有$ss_c=\tilde{ss}_c$。然而对于$(R,c)=(\mathbb{Z},3)$，计算结果表明$ss_3$不是切片环面的，这意味着它与约化不变量线性无关，特别是与Rasmussen不变量线性无关。
英文摘要：
We give a family of slice-torus invariants $\tilde{ss}_c$, each defined from the $c$-divisibility of the reduced Lee class in a variant of reduced Khovanov homology, parameterized by prime elements $c$ in any principal ideal domain $R$. For the special case $(R, c) = (F[H], H)$ where $F$ is any field, we prove that $\tilde{ss}_c$ coincides with the Rasmussen invariant $s^F$ over $F$. Compared with the unreduced invariants $ss_c$ defined by the first author in a previous paper, we prove that $ss_c = \tilde{ss}_c$ for $(R, c) = (F[H], H)$ and $(\mathbb{Z}, 2)$. However for $(R, c) = (\mathbb{Z}, 3)$, computational results show that $ss_3$ is not slice-torus, which implies that it is linearly independent from the reduced invariants, and particularly from the Rasmussen invariants.
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