$\mathfrak{sl}(N)$–link homology ($N\geq 4$) using foams and the Kapustin–Li formula

Abstract

We use foams to give a topological construction of a rational link homology categorifying the $\mathfrak{s}\mathfrak{l}\left(N\right)$ link invariant, for $N\ge 4$. To evaluate closed foams we use the Kapustin–Li formula adapted to foams by Khovanov and Rozansky [Adv. Theor. Math. Phys. 11 (2007) 233-259]. We show that for any link our homology is isomorphic to the Khovanov–Rozansky [Fund. Math. 199 (2008) 1-91] homology.