Summary
A mathematical knot is obtained by taking a piece of rope, tangling it in some way, and then joining the ends. A classical question in knot theory asks whether two knots can be obtained from each other by continuously transforming the rope. One way to distinguish two knots is to compute their knot invariants. Some of the most powerful knot invariants include the HOMFLY polynomial and its recent generalization known as Khovanov–Rozansky homology. For instance, the HOMFLY polynomial is used in molecular biology to study how DNA molecules are folded in space. In this project, we relate these knot
