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Quantum (sln, ∧V n) link invariant and matrix factorizations

Published online by Cambridge University Press:  11 January 2016

Yasuyoshi Yonezawa
Yasuyoshi Yonezawa*
Affiliation:
Graduate School of Mathematics, Nagoya University, Nagoya 464-8602, Japanyasuyoshi.yonezawa@math.nagoya-u.ac.jp
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Abstract

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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.

Keywords

57M25
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 204 , December 2011 , pp. 69 - 123
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

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