MIT Geometry and Topology Seminar

Monday, March 20, 2023 at 3:00pm

Building 2, 2-449

Speaker: Sally Collins

Title: Homology cobordism & knot concordance

Abstract: We can associate to a knot K in the 3-sphere a 3-manifold, called the zero-surgery of K, via performing zero-framed Dehn surgery on the knot. It is a natural question to ask: if two knots have zero-surgeries which are homology cobordant via a cobordism that preserves the homology class of the two positively oriented knot meridians, does that imply that the knots must be smoothly concordant? We review the history and motivation of this question and questions like it and describe our own result, ending with a brief discussion of a proof technique of obstructing torsion in the smooth concordance group.

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