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

中文翻译：

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sl(P)$\mathfrak {sl}(P)$ 特征 P$P$ 链接同源性的分裂链接检测

我们根据链接的减少提供了链接分裂的充分条件$\mathfrak{sl}(否)$链接与任意场系数的同源性。充分性证明使用 Dowlin 谱序列和带扭曲系数的缝合 Floer 同源性。如果$否$是质数，系数域是特征域$否$，那么分裂的充分条件也是必要的。什么时候$否=\mathrm{2个}$, 我们用$\mathbf{Z}/\mathrm{2个}$ 系数。