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Topology/Geometry Seminar

Using surgery to study unknotting with a single twist

Samantha Allen (Dartmouth)

Location:  zoom link: https://rutgers.zoom.us/j/96007672653?pwd=UkhZV0l0WWNVenFqY1FYdjVydkVyQT09
Date & time: Tuesday, 13 April 2021 at 3:50PM - 4:50PM

Ohyama showed that any knot can be unknotted by performing two full twists, each on a set of parallel strands. We consider the question of whether or not a given knot can be unknotted with a single full twist, and if so, what are the possible linking numbers associated to such a twist. It is observed that if a knot can be unknotted with a single twist, then some surgery on the knot bounds a rational homology ball. Using tools such as classical invariants and invariants arising from Heegaard Floer theory, we give obstructions for a knot to be unknotted with a single twist of a given linking number. In this talk, I will discuss some of these obstructions, their implications (especially for alternating knots), many examples, and some unanswered questions. This talk is based on joint work with Charles Livingston.