Relative Khovanov-Jacobsson classes

Abstract

To a smooth, compact, oriented, properly-embedded surface in the $4$-ball, we define an invariant of its boundary-preserving isotopy class from the Khovanov homology of its boundary link. Previous work showed that when the boundary link is empty, this invariant is determined by the genus of the surface. We show that this relative invariant: can obstruct sliceness of knots; detects a pair of slices for $9_{46}$; is not hindered by detecting connected sums with knotted $2$-spheres.

arXiv comment16 pages, 11 figures

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Cited by in corpus (4)

• A mixed invariant of non-orientable surfaces in equivariant Khovanov homology
• Categorical lifting of the Jones polynomial: a survey
• Homotopy ribbon discs with a fixed group
• Homotopy functoriality for Khovanov spectra