Nagoya Mathematical Journal

Quantum (sln,Vn) link invariant and matrix factorizations

Yasuyoshi Yonezawa

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In this paper, we give a generalization of Khovanov-Rozansky homology. We define a homology associated to the quantum (sln,Vn) link invariant, where Vn is the set of fundamental representations of Uq(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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Nagoya Math. J., Volume 204 (2011), 69-123.

First available in Project Euclid: 5 December 2011

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Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}


Yonezawa, Yasuyoshi. Quantum $(\mathfrak{sl}_{n},\wedge V_{n})$ link invariant and matrix factorizations. Nagoya Math. J. 204 (2011), 69--123. doi:10.1215/00277630-1431840.

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