Khovanov–Rozansky homology for embedded graphs
Volume 214 / 2011
Fundamenta Mathematicae 214 (2011), 201-214
MSC: Primary 57M27.
DOI: 10.4064/fm214-3-1
Abstract
For any positive integer $n$, Khovanov and Rozansky constructed a bigraded link homology from which you can recover the $\mathfrak{sl}_n$ link polynomial invariants. We generalize the Khovanov–Rozansky construction in the case of finite 4-valent graphs embedded in a ball $B^3 \subset \mathbb{R}^3$. More precisely, we prove that the homology associated to a diagram of a 4-valent graph embedded in $B^3\subset \mathbb{R}^3$ is invariant under the graph moves introduced by Kauffman.
