# 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

#### Citations

##### Publications citing this paper.

SHOWING 1-10 OF 10 CITATIONS

## Concordances from differences of torus knots to $L$-space knots

VIEW 6 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## On the secondary Upsilon invariant.

VIEW 4 EXCERPTS

CITES BACKGROUND

HIGHLY INFLUENCED

## Chiral smoothings of knots.

VIEW 1 EXCERPT

CITES METHODS

## Minimal braid representatives of quasipositive links

VIEW 1 EXCERPT

CITES BACKGROUND

## On a Nonorientable Analogue of the Milnor Conjecture

VIEW 2 EXCERPTS

CITES METHODS

## Quasi-positivity and recognition of products of conjugacy classes in free groups

VIEW 1 EXCERPT

CITES BACKGROUND

## Upsilon type concordance invariants

VIEW 2 EXCERPTS

CITES METHODS

## Complex projective plane curves and low-dimensional topology

VIEW 2 EXCERPTS

CITES BACKGROUND & METHODS

#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 37 REFERENCES

## The Upsilon function of L-space knots is a Legendre transform

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## d-invariants and deformations of cuspidal singular points of plane curves

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Quasipositivity as an obstruction to sliceness

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## Concordance homomorphisms from knot Floer homology

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Math

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Embedded annuli and Jones’ conjecture

VIEW 3 EXCERPTS

HIGHLY INFLUENTIAL

## Minimal braid representatives of quasipositive links

VIEW 1 EXCERPT