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Adam Lowrance, Vassar College, & Min Hoon Kim, Korea Institute for Advanced Study – Triangle Topology Seminar
October 16, 2018 @ 3:30 pm - 6:00 pm
Triangle Topology Seminar
Location: SAS 2102, North Carolina State University
3:30 pm – 4:30 pm
Speaker: Adam Lowrance, Vassar College
Title: Gordian distance and spectral sequences in Khovanov homology
Abstract: The Gordian distance between two knots is the fewest number of crossing changes necessary to transform one knot into the other. Khovanov homology is a categorification of the Jones polynomial that comes equipped with several spectral sequences. In this talk, we show that the page at which some of these spectral sequences collapse gives a lower bound on the Gordian distance between a given knot and the set of alternating knots (and also on other related Gordian distances). We also discuss connections to the existence of torsion in Khovanov homology.
4:45 pm – 5:45 pm
Speaker: Min Hoon Kim, Korea Institute for Advanced Study
Title: A family of freely sliced good boundary links
Abstract: The still open topological surgery conjecture for 4-manifolds is equivalent to the statement that all good boundary links are freely slice. In this talk, I will show that every good boundary link with a pair of derivative links on a Seifert surface satisfying a homotopically trivial plus assumption is freely slice. This subsumes all previously known methods for freely slicing good boundary links with two or more components, and provides new freely slice links. This is joint work with Jae Choon Cha and Mark Powell.