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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-3-1,
author = {Emmanuel Wagner},
title = {Khovanov-Rozansky homology for embedded graphs},
journal = {Fundamenta Mathematicae},
volume = {215},
year = {2011},
pages = {201-214},
zbl = {1235.57012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-3-1}
}
Emmanuel Wagner. Khovanov-Rozansky homology for embedded graphs. Fundamenta Mathematicae, Tome 215 (2011) pp. 201-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm214-3-1/