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Keywords = Khovanov homology

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19 pages, 306 KiB  
Article
Khovanov Homology of Three-Strand Braid Links
by Young Chel Kwun, Abdul Rauf Nizami, Mobeen Munir, Zaffar Iqbal, Dishya Arshad and Shin Min Kang
Symmetry 2018, 10(12), 720; https://doi.org/10.3390/sym10120720 - 5 Dec 2018
Viewed by 3515
Abstract
Khovanov homology is a categorication of the Jones polynomial. It consists of graded chain complexes which, up to chain homotopy, are link invariants, and whose graded Euler characteristic is equal to the Jones polynomial of the link. In this article we give some [...] Read more.
Khovanov homology is a categorication of the Jones polynomial. It consists of graded chain complexes which, up to chain homotopy, are link invariants, and whose graded Euler characteristic is equal to the Jones polynomial of the link. In this article we give some Khovanov homology groups of 3-strand braid links Δ 2 k + 1 = x 1 2 k + 2 x 2 x 1 2 x 2 2 x 1 2 x 2 2 x 1 2 x 1 2 , Δ 2 k + 1 x 2 , and Δ 2 k + 1 x 1 , where Δ is the Garside element x 1 x 2 x 1 , and which are three out of all six classes of the general braid x 1 x 2 x 1 x 2 with n factors. Full article
(This article belongs to the Special Issue Symmetry in Applied Mathematics)
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