特征P$P$中sl(P)$\mathfrak {sl}(P)$链路同源性的分离链路检测

Pub Date : 2023-05-31 DOI:10.1112/topo.12297
Joshua Wang
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引用次数: 0

摘要

我们根据具有任意域系数的约化sl(N)$\mathfrak{sl}(N)$链路同调,给出了一个链路可分裂的充分条件。充分性的证明使用道林谱序列和具有扭曲系数的缝合Floer同源性。如果N$N$是素数,并且系数域具有特征N$N$N,则分裂性的充分条件也是必要的。当N=2$N=2$时,我们恢复了Lipshitz–Sarkar对具有Z/2$\mathbf{Z}/2$系数的Khovanov同源性的分裂链检测结果。
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Split link detection for sl ( P ) $\mathfrak {sl}(P)$ link homology in characteristic P $P$

We provide a sufficient condition for splitness of a link in terms of its reduced sl ( N ) $\mathfrak {sl}(N)$ link homology with arbitrary field coefficients. The proof of sufficiency uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. If N $N$ is prime and the coefficient field is of characteristic N $N$ , then the sufficient condition for splitness is also necessary. When N = 2 $N = 2$ , we recover Lipshitz–Sarkar's split link detection result for Khovanov homology with Z / 2 $\mathbf {Z}/2$  coefficients.

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