In November 2022 I gave a zoom talk in the Oklahoma State University Topology seminar. It was on 9 November, although it was the 8th at the time in Oklahoma.
Title: Symplectic structures in hyperbolic 3-manifold triangulations
Abstract: In the 1980s, Neumann and Zagier introduced a symplectic vector space associated to an ideal triangulation of a cusped 3-manifold, such as a knot complement. We give an interpretation for this symplectic structure in terms of the topology of the 3-manifold, via intersections of certain curves on a Heegaard surface. We also give an algorithm to construct curves forming a symplectic basis for this vector space. This approach gives a description of hyperbolic structures on a knot complement via Ptolemy equations, which can be used to calculate the A-polynomial. This talk involves joint work with Jessica Purcell, Joshua Howie and Yi Huang.
Slides from the talk are below.22-11-08_oklahoma_talk_slides