# Khovanov homology and ribbon concordances

@article{Levine2019KhovanovHA, title={Khovanov homology and ribbon concordances}, author={Adam Simon Levine and Ian Zemke}, journal={Bulletin of the London Mathematical Society}, year={2019}, volume={51} }

We show that a ribbon concordance between two links induces an injective map on Khovanov homology.

## 29 Citations

### Homotopy ribbon concordance and Alexander polynomials

- MathematicsArchiv der Mathematik
- 2020

We show that if a link J in the 3-sphere is homotopy ribbon concordant to a link L, then the Alexander polynomial of L divides the Alexander polynomial of J.

### Ribbon distance and Khovanov homology

- MathematicsAlgebraic & Geometric Topology
- 2020

We study a notion of distance between knots, defined in terms of the number of saddles in ribbon concordances connecting the knots. We construct a lower bound on this distance using the X-action on…

### Link homology theories and ribbon concordances

- MathematicsQuantum Topology
- 2022

It was recently proved by several authors that ribbon concordances induce injective maps in knot Floer homology, Khovanov homology, and the Heegaard Floer homology of the branched double cover. We…

### Homotopy functoriality for Khovanov spectra

- MathematicsJournal of Topology
- 2022

We prove that the Khovanov spectra associated to links and tangles are functorial up to homotopy and sign.

### Heegaard Floer homology and ribbon homology cobordisms

- Mathematics
- 2019

It has recently been shown by several authors that ribbon concordances, or certain variants thereof, induce an injection on knot homology theories. We prove a variant of this for Heegaard Floer…

### A mixed invariant of non-orientable surfaces in equivariant Khovanov homology

- Mathematics
- 2021

. We construct a mixed invariant of nonorientable surfaces from the Lee and Bar-Natan deformations of Khovanov homology and use it to distinguish pairs of surfaces bounded by the same knot, including…

### Ribbon concordance and the minimality of tight fibered knots

- Mathematics
- 2022

. Agol proved that ribbon concordance forms a partial ordering on the set of knots in the 3-sphere. In this paper, we prove that all tight ﬁbered knots are minimal in this partially ordered set. We…

### Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

- MathematicsCanadian Journal of Mathematics
- 2021

Abstract We establish homotopy ribbon concordance obstructions coming from the Blanchfield form and Levine–Tristram signatures. Then, as an application of twisted Alexander polynomials, we show that…

### Ribbon cobordisms as a partial order

- Mathematics
- 2022

. We show that the notion of ribbon rational homology cobordism yields a partial order on the set of aspherical 3-manifolds, thus supporting a conjecture formulated by Daemi, Lidman, Vela-Vick and…

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