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BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

A note on the Upsilon invariant, its homogenization, and the braid index of knots (Feller/Krcatovich) Feller, Peter

Description

We use Ozsvath, Stipsicz, and Szabo's Upsilon invariant to provide bounds on cobordisms between knots that `contain full-twists'. This generalizes previous results and allows us to recover and generalize a classical consequence of the Morton-Franks-Williams inequality for knots: positive braids that contain a full twist realize the braid index of their closure. We also provide inductive formulas for the Upsilon invariants of torus knots and compare the Upsilon function to the Levine-Tristram signature profile.

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