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.
Original language | English (US) |
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Pages (from-to) | 217-246 |
Number of pages | 30 |
Journal | Journal fur die Reine und Angewandte Mathematik |
Volume | 2024 |
Issue number | 809 |
DOIs | |
State | Published - Apr 1 2024 |
All Science Journal Classification (ASJC) codes
- General Mathematics
- Applied Mathematics