The A-Polynomial and Knot Volume

Marc Schilder (Buffalo)

Abstract: The A-polynomial is a knot invariant which has interesting connections to the hyperbolic geometry of a knot exterior, though computing the A-polynomial remains difficult in many cases. I will provide a formula for computing A-polynomials of graph knots, as well as winding number zero satellites of graph knots in terms of other A-polynomials. We then will discuss a conjectured relationship between the logarithmic Mahler measure of the A-polynomial and the hyperbolic volume of the knot exterior.