turkmath.org

Given any knot $K \subset S^3$, there are different ways of representing these knots and each one of them has its own advantage. A grid diagram is a piecewise linear, planar or toroidal representation of a knot using an nxn grid with $X$ and $O$-markings, following a certain convention about the over/under crossings and the orientation of the knot. Transverse knots form a special family of knots living in $S^3$ equipped with a contact structure. We can represent transverse knots with grid diagrams as well. Grid homology associated to a grid representation of a given knot provides an invariant of the knot which can be computed combinatorially. This feature of grid homology yields to certain computational advantages. From this structure, one can extract this numerical invariant $\theta(K)$ for any knot $K$ which detects the transverse simplicity. If time permits, I will present an example to demonstrate the efficiency of grid homology method to determine the transverse simplicity of a knot type.