Split link detection for sl(P)$\mathfrak {sl}(P)$ link homology in characteristic P$P$

Abstract

We provide a sufficient condition for splitness of a link in terms of its reduced frakturslfalse(Nfalse)$\mathfrak {sl}(N)$ 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 boldZ/2$\mathbf {Z}/2$ coefficients.