A Link Splitting Spectral Sequence in Khovanov Homology

Abstract

We construct a new spectral sequence beginning at the Khovanov homology of a link and converging to the Khovanov homology of the disjoint union of its components. The page at which the sequence collapses gives a lower bound on the splitting number of the link, the minimum number of times its components must be passed through one another in order to completely separate them. In addition, we build on work of Kronheimer-Mrowka and Hedden-Ni to show that Khovanov homology detects the unlink.

36 pages, 15 figures. Includes table of computations

References in corpus (2)

• Khovanov module and the detection of unlinks
• Nilpotent slices, Hilbert schemes, and the Jones polynomial

Cited by in corpus (25)

• Sequencing BPS Spectra
• Hilbert schemes and $y$-ification of Khovanov-Rozansky homology
• Functoriality of colored link homologies
• Instanton Floer homology for sutured manifolds with tangles
• Immersed concordances of links and Heegaard Floer homology
• Khovanov homology detects the figure-eight knot
• Dualizable link homology
• Splitting numbers of links
• Blanchfield forms and Gordian distance
• Tautological classes and symmetry in Khovanov-Rozansky homology
• Categorical lifting of the Jones polynomial: a survey
• Khovanov homology detects split links
• Rank Bounds in Link Floer Homology and Detection Results
• Links of Second Smallest Knot Floer Homology
• On Khovanov Homology and Related Invariants
• Twisted Alexander invariants detect trivial links
• Structures in HOMFLY-PT homology
• Curved Rickard complexes and link homologies
• Two detection results of Khovanov homology on links
• HOMFLYPT Homology over ${\mathbb{Z}}_2$ Detects Unlinks
• An Exceptional Splitting of Khovanov's Arc Algebras in Characteristic 2
• Closures of $3$-braids and detection
• A specious unlinking strategy
• Splitting numbers and signatures
• Betti Numbers of the HOMFLYPT Homology