Khovanov homology and ribbon concordances

Abstract

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

Homotopy ribbon concordance and Alexander polynomials

“…A number of articles have recently appeared on the relation of smooth ribbon concordance to Heegaard-Floer and Khovanov homology [9,14,17,19,21]. These techniques of course do not apply to locally flat concordances.…”

Ascent concordance

“…is map is de ned by spli ing (S, M) into strict pieces, and concatenating the maps assigned to these pieces using the identity of their domains and domains given in Proposition 3. 13. ♦ e map assigned to a pseudostrict cobordism enjoys the factoring property, described in Proposition 3.11, by construction.…”

Homotopy ribbon concordance, Blanchfield pairings, and twisted Alexander polynomials

“…We have H 1 (K ; Z) ∼ = Z/9 ⊕ Z/9 and deg 1/3 (K ) = 4, η 1/3 (K ) = 2, σ 1/3 (K ) = 0, so Propositions 3.2 and 3.3 do not obstruct K ≥ top K. One may check that K is not ribbon concordant to K, e.g. using Khovanov homology [LZ19]. However, we do not know the answer to the following.…”