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

Abstract

AbstractWe provide a sufficient condition for splitness of a link in terms of its reduced link homology with arbitrary field coefficients. The proof of sufficiency uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. If is prime and the coefficient field is of characteristic , then the sufficient condition for splitness is also necessary. When , we recover Lipshitz–Sarkar's split link detection result for Khovanov homology with coefficients.