BIRS Workshop Lecture Videos

Banff International Research Station Logo

BIRS Workshop Lecture Videos

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


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.

Item Media

Item Citations and Data


Attribution-NonCommercial-NoDerivatives 4.0 International