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Split link detection for sl(P)$\mathfrak {sl}(P)$ link homology in characteristic P$P$
Journal of Topology ( IF 0.8 ) Pub Date : 2023-05-31 , DOI: 10.1112/topo.12297
Joshua Wang 1
Affiliation  

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.

中文翻译:

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 sl ( ) $\mathfrak {sl}(N)$ 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 $N$ 是质数,系数域是特征域 $N$ ,那么分裂的充分条件也是必要的。什么时候 = 2个 $N = 2$ , 我们用 Z / 2个 $\mathbf {Z}/2$  系数。
更新日期:2023-06-01
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