On Khovanov Homology and Related Invariants

This paper begins with a survey of some applications Khovanov homology to low-dimensional topology, an eye toward extending these results \(\mathfrak {sl}(n)\) homologies. We extend Levine-Zemke’s ribbon concordance obstruction from foam homologies for n ≥ 2, including the universal {sl}(2)\) and {sl}(3)\) theories. Inspired by Alishahi Dowlin’s bounds unknotting number coming relying on spectral sequence arguments, we produce alternation knot. Lee Bar-Natan sequences also provide lower Turaev genus.