The A-polynomial is a knot invariant built from character varieties of knot complements. When it was first constructed, it was believed to be independent of Reshetikhin-Turaev invariants such as the Jones polynomial. Now we understand that the close relationship between these invariants only manifests after they're both quantised. This talk will recall the A-polynomial and explain a novel procedure for quantising it that relies heavily on defects in skein theory.
This is based on joint work with David Jordan.
