论文标题
部分可观测时空混沌系统的无模型预测
A new presentation of the osp(1|2)-polynomial link invariant and categorification
论文作者
论文摘要
OSP（1 | 2n）多项式结$ j_k^n $与so（2n+1）结不变$ {} _ {so} j_k^n $ clark in arxiv：15099.03533和arxiv中的blumen in arxiv：09001.332323232。在等级的情况下，未颜色的$ u_ {q}（osp（1 | 2））$ link不变性等于$ u_ {t^{ - 1} q} q}（sl_2）$ link link不变，其中$ t^2 = -1 $。我们定义了类似于Kauffman支架的绞线关系，并使用它来恢复与Clark的未颜色的OSP（1 | 2） - 链接不变式相吻合。该定义还来自$ u_ {q，π}（sl_2）$的表示理论，但使用克拉克的不同方法。我们证明，我们的不变式很容易被稍微修改的Khovanov同源性版本分类，该版本配备了额外的$ \ mathbb {z} _4 $ -grading。我们还构建了Putyra的覆盖khovanov同源性的类似修改版本，来自Arxiv：1310.1895。这表明两个不变性之间的相似性在分类级别也保持。
There is a known connection between the osp(1|2n) polynomial knot invariant $J_K^n$ and the so(2n+1) knot invariant ${}_{so} J_K^n$ studied by Clark in arXiv:1509.03533 and Blumen in arXiv:0901.3232. In the rank one case, the uncolored $U_{q}(osp(1|2))$ link invariant is equal to the $U_{t^{-1}q}(sl_2)$ link invariant where $t^2=-1$. We define a skein relation similar to the Kauffman bracket, and use that to recover an oriented link invariant which coincides with Clark's uncolored osp(1|2)-link invariant. This definition also comes from the representation theory of $U_{q,π}(sl_2)$, but using different methods from Clark. We show that our invariant is easily categorified by a slightly modified version of Khovanov homology equipped with an extra $\mathbb{Z}_4$-grading. We also construct a similarly modified version of Putyra's covering Khovanov homology from arXiv:1310.1895. This suggests that the similarity between the two invariants holds at the categorified level as well.
