Ascent concordance

A cobordism between links in thickened surfaces consists of a surface $ S and $3$-manifold $M $, with properly embedded M \times I $. We show that there exist such if $(S,M) is them which simple, then must be complex. That is, are cases low complexity the does not imply $3$-manifold. Specifically, we concordant concordance can only realised by passing through thickenings higher genus surfaces. exhibit an infinite family detected elementary method other families detectable this way. investigate augmented version Khovanov homology, use it to detect these families. Such provide counterexamples analogue Slice-Ribbon conjecture.