On $\mathfrak{sl}(N)$ link homology with mod $N$ coefficients

Abstract

We construct an operator on $\mathfrak{sl}(N)$ link homology with coefficients in a ring whose characteristic divides $N$. If $P$ is a prime number, we use this operator to exhibit structural features of $\mathfrak{sl}(P)$ link homology that are special to characteristic $P$ that generalize well-known features of Khovanov homology that are special to characteristic 2.