*Article* **Khovanov Homology of Three-Strand Braid Links**

#### **Young Chel Kwun 1, Abdul Rauf Nizami 2, Mobeen Munir 3,\* , Zaffar Iqbal 4, Dishya Arshad 3 and Shin Min Kang 5,6,\***


Received: 7 November 2018; Accepted: 15 November 2018; Published: 5 December 2018

**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 Khovanov homology groups of 3-strand braid links Δ2*k*+<sup>1</sup> = *x*2*k*+<sup>2</sup> 1 *<sup>x</sup>*2*<sup>x</sup>*21*x*22*x*21 ··· *x*22*x*21*x*21, <sup>Δ</sup>2*k*+1*x*2, and <sup>Δ</sup>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.

**Keywords:** Khovanov homology; braid link; Jones polynomial

**MSC:** 57M27; 55N20
