Nagoya Mathematical Journal

Quantum (sln,∧Vn) link invariant and matrix factorizations

Yasuyoshi Yonezawa

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Abstract

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.

Article information

Source
Nagoya Math. J., Volume 204 (2011), 69-123.

Dates
First available in Project Euclid: 5 December 2011

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1323107838

Digital Object Identifier
doi:10.1215/00277630-1431840

Mathematical Reviews number (MathSciNet)
MR2863366

Zentralblatt MATH identifier
1271.57033

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

Citation

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. https://projecteuclid.org/euclid.nmj/1323107838


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Nagoya Mathematical Journal

Nagoya Mathematical Journal
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