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The A-Polynomial and Knot Volume

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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.