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Topology/Geometry Seminar

Detection of essential punctured tori in hyperbolic knot complements

Yi Wang (UPenn)

Location:  Hill 705
Date & time: Tuesday, 05 December 2023 at 4:00PM - 5:00PM

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.