On cobordisms between knots, braid index, and the Upsilon-invariant

@article{Feller2017OnCB,
  title={On cobordisms between knots, braid index, and the Upsilon-invariant},
  author={Peter Feller and David Krcatovich},
  journal={Mathematische Annalen},
  year={2017},
  volume={369},
  pages={301-329}
}
We use Ozsváth, Stipsicz, and Szabó’s Upsilon-invariant to provide bounds on cobordisms between knots that ‘contain full-twists’. In particular, we recover and generalize a classical consequence of the Morton–Franks–Williams inequality for knots: positive braids that contain a positive full-twist realize the braid index of their closure. We also establish that quasi-positive braids that are sufficiently twisted realize the minimal braid index among all knots that are concordant to their closure… CONTINUE READING
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