Punctured JSJ tori and tautological extensions of Azumaya algebras

Yi Wang (Penn)

Abstract: The SL_2(C) canonical component of a hyperbolic knot group is an affine algebraic curve. The theory of Culler-Shalen associates essential surfaces to ideal points of this curve, and it is a subtle problem to determine which surfaces are detected through this process. We will show that families of punctured tori that cap off to a system of JSJ tori under exceptional Dehn filling are detected by the Culler-Shalen machine. In addition, we will discuss how this result refines arithmetic invariants on the SL_2(C) canonical component defined by Chinburg-Reid-Stover.