A mixed invariant of non-orientable surfaces in equivariant Khovanov homology

Abstract

We construct a mixed invariant of non-orientable surfaces from the Lee and Bar-Natan deformations of Khovanov homology and use it to distinguish pairs of surfaces bounded by the same knot, including some exotic examples.

43 pages, 7 figures. V2: improved citations. V3: minor revisions. Accepted for publication in the Transactions of the AMS

References in corpus (5)

• The Karoubi envelope and Lee's degeneration of Khovanov homology
• Khovanov's invariant for closed surfaces
• Relative Khovanov-Jacobsson classes
• Concordance invariants from the $E(-1)$ spectral sequence on Khovanov homology
• New Heegaard Floer slice genus and clasp number bounds

Cited by in corpus (2)

• Categorical lifting of the Jones polynomial: a survey
• Homotopy ribbon discs with a fixed group