Abstract
AbstractIn this paper, we give a generalization of Khovanov-Rozansky homology. We define a homology associated to the quantum (sln, ∧Vn) link invariant, where∧Vnis the set of fundamental representations ofUq(sln). In the case of an oriented link diagram composed of[k, 1]-crossings, we define a homology and prove that the homology is invariant under Reidemeister II and III moves. In the case of an oriented link diagram composed of general[i,j]-crossings, we define a normalized Poincaré polynomial of homology and prove that the normalized Poincaré polynomial is a link invariant.
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