论文标题
李班的分裂性的一家不变的家族
A family of slice-torus invariants from the divisibility of Lee classes
论文作者
论文摘要
我们给出了一个slice torus forpariants $ \ tilde {ss} _c $，每个都从$ c $ - 可降低的Lee类的$ c $ - 可定义性中定义，以降低的Khovanov同源性变体，在任何主要的主要理想域$ r $ r $中，由Prime Elements $ C $参数化。对于特殊情况$（r，c）=（f [h]，h）$，其中$ f $是任何字段，我们证明$ \ tilde {ss} _C $与$ f $上的rasmussen不变性$ s^f $重合。与上一篇论文中第一作者定义的未恢复不变的$ ss_c $相比，我们证明$ ss_c = \ tilde {ss} _c $ for $（r，c）=（r，c）=（f [h]，h），h）$ and $（\ mathbb {z}，2）$。但是，对于$（r，c）=（\ mathbb {z}，3）$，计算结果表明$ ss_3 $不是slice trice-torus，这意味着它与减少的不变式是线性独立的，尤其是与rasmussen不变的无关。
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.
