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.

arXiv comment43 pages, 7 figures. V2: improved citations. V3: minor revisions. Accepted for publication in the Transactions of the AMS

References in corpus (17)

• Khovanov's homology for tangles and cobordisms
• An invariant of link cobordisms from Khovanov homology
• Khovanov module and the detection of unlinks
• Fixing the functoriality of Khovanov homology
• The Karoubi envelope and Lee's degeneration of Khovanov homology
• Unoriented topological quantum field theory and link homology
• Khovanov homology and ribbon concordance
• The Bar-Natan homology and unknotting number
• Khovanov's invariant for closed surfaces
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Ribbon distance and Khovanov homology
• Knotted surfaces in 4-manifolds and stabilizations
• Relative Khovanov-Jacobsson classes
• Transverse invariants and exotic surfaces in the 4-ball
• Concordance invariants from the $E(-1)$ spectral sequence on Khovanov homology
• Exotically knotted disks and complex curves
• 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