Khovanov homology and exotic surfaces in the 4-ball
arXiv:2108.04810
Abstract
We show that the cobordism maps on Khovanov homology can distinguish smooth surfaces in the 4-ball that are exotically knotted (i.e., isotopic through ambient homeomorphisms but not ambient diffeomorphisms). We develop new techniques for distinguishing cobordism maps on Khovanov homology, drawing on knot symmetries and braid factorizations. We also show that Plamenevskaya's transverse invariant in Khovanov homology is preserved by maps induced by positive ascending cobordisms.
31 pages, 14 figures, 5 tables, 2 appendices, 2 footnotes. v2 additional braided perspective, minor expositional changes