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December 2011 Quantum (sln,Vn) link invariant and matrix factorizations
Yasuyoshi Yonezawa
Nagoya Math. J. 204: 69-123 (December 2011). DOI: 10.1215/00277630-1431840

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.

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Yasuyoshi Yonezawa. "Quantum (sln,Vn) link invariant and matrix factorizations." Nagoya Math. J. 204 69 - 123, December 2011. https://doi.org/10.1215/00277630-1431840

Information

Published: December 2011
First available in Project Euclid: 5 December 2011

zbMATH: 1271.57033
MathSciNet: MR2863366
Digital Object Identifier: 10.1215/00277630-1431840

Subjects:
Primary: 57M25

Rights: Copyright © 2011 Editorial Board, Nagoya Mathematical Journal

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Vol.204 • December 2011
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