Split link detection for sl(P) link homology in characteristic P

TL;DR

This paper proves that reduced sl(P) link homology over Z/P coefficients detects split links, extending known results for Khovanov homology at P=2 to all primes P using spectral sequences and sutured Floer homology.

Contribution

It generalizes split link detection from Khovanov homology to reduced sl(P) homology for all prime P, employing spectral sequences and sutured Floer homology techniques.

Findings

Reduced sl(P) homology detects split links for prime P.

Recovers Lipshitz-Sarkar's result at P=2.

Extends detection results to all prime characteristics.

Abstract

If $P$ is a prime number, we show that reduced $\mathfrak{sl}(P)$ link homology with coefficients in $\mathbf{Z}/P$ detects split links. The argument uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. When $P = 2$, we recover Lipshitz-Sarkar's split link detection result for Khovanov homology with $\mathbf{Z}/2$ coefficients.