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Algebra/Topology Seminar – Patricia Cahn (Smith College)
February 19, 2018 @ 11:00 am - 12:00 pm
Title: Colored Tri-Plane Diagrams and the Slice-Ribbon Problem
Abstract: We study dihedral branched covers of the four-dimensional sphere, where the branching set is a surface with one singularity modeled on the cone on a knot K. We construct examples of these covers using colored tri-plane diagrams, which are triples of tangles that can be used to describe a surface in the four-sphere. We also show that a knot invariant arises in this context, which can potentially be used to prove that a slice knot is not ribbon.