Twisting, ladder graphs and A-polynomials

Emily Thompson (Monash)

Abstract: The A-polynomial is a powerful knot invariant that captures information about the geometry and topology of a knot complement, however, it remains difficult to compute in general. In this talk we will see connections between the equations defining the A-polynomial, layered solid tori, and cluster algebras. Drawing on these connections, I will outline my result that allows us to simplify the calculations of A-polynomials for infinite families of knots related by twisting. I will give an idea of the proof, which uses perfect matchings of weighted ladder graphs, and demonstrate the method in the case of a family of twisted torus knots.