Narrow Results

In this paper, we shall give an explicit Gauss diagram formula for the Kontsevich integral of links up to degree four. This practical formula enables us to actually compute the Kontsevich integral in a combinatorial way.

In this paper, we give a combinatorial description of the concordance invariant $𝜀$ defined by Hom, prove some properties of this invariant using grid homology techniques. We compute the value of $𝜀$ for $(p,q)$ torus knots and prove that $𝜀({𝔾}_{+})=1$ if ${𝔾}_{+}$ is a grid diagram for a positive braid. Furthermore, we show how $𝜀$ behaves under $(p,q)$-cabling of negative torus knots.

This article delivers about the number of advanced computational biology courses in NUS.