#### Volume 13, issue 2 (2009)

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

### Marco Mackaay, Marko Stošić and Pedro Vaz

Geometry & Topology 13 (2009) 1075–1128
##### 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.

##### Keywords
\mathfraksl(N), foams, link homology, Kapustin–Li, Khovanov–Rozansky
##### Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57M25, 81R50, 18G60