On the integral of $\log x\frac{dy}{y}-\log y\frac{dx}{x}$ over the A-polynomial curves

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/174340In this note, we study the integral of the 1-form $\log x\frac{dy}{y}-\log y\frac{dx}{x}$ over certain plane curves defined by A-polynomials of knots. It is quite surprising that a Chern-Simons type invariant of 3-manifolds, which can be geometrically computed, may be used to get the exact values of those integrals. The arithmetic nature of these integrals is still unknown at the moment and deserved further investigation.To appear in the Proceedings of the International Conference on Quantum TopologyGeometric Topology57M27; 57M05On the integral of $\log x\frac{dy}{y}-\log y\frac{dx}{x}$ over the A-polynomial curvestext