Khovanov homology and exotic surfaces in the 4-ball

Kyle Hayden; Isaac Sundberg

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arXiv · 2108.04810

Khovanov homology and exotic surfaces in the 4-ball

Kyle Hayden·Isaac Sundberg

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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.

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Kyle Hayden, Isaac Sundberg. 2021-08-10. Khovanov homology and exotic surfaces in the 4-ball. https://arxiv.org/abs/2108.04810

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