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Khovanov-Rozansky homology for embedded graphs

Emmanuel Wagner — 2011

Fundamenta Mathematicae

For any positive integer n, Khovanov and Rozansky constructed a bigraded link homology from which you can recover the 𝔰𝔩ₙ link polynomial invariants. We generalize the Khovanov-Rozansky construction in the case of finite 4-valent graphs embedded in a ball B³ ⊂ ℝ³. More precisely, we prove that the homology associated to a diagram of a 4-valent graph embedded in B³ ⊂ ℝ³ is invariant under the graph moves introduced by Kauffman.

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