Khovanov module and the detection of unlinks

Abstract

We study a module structure on Khovanov homology, which we show is natural under the Ozsvath-Szabo spectral sequence to the Floer homology of the branched double cover. As an application, we show that this module structure detects trivial links. A key ingredient of our proof is that the H_1/Torsion module structure on Heegaard Floer homology detects S^1xS^2 connected summands.

47 pages, 4 figures; Corrected error in the proof that the Khovanov module is a link invariant; Added details on homological cancellation in the presence of a filtration; Introduction revised; Typos and minor errors corrected

References in corpus (3)

• Floer homology and knot complements
• Géométrie de contact: de la dimension trois vers les dimensions supérieures
• Heegaard Floer homologies and contact structures

Cited by in corpus (26)

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• Functoriality of colored link homologies
• Instanton Floer homology for sutured manifolds with tangles
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• Instantons and Annular Khovanov Homology
• Divisibility of Lee's class and its relation with Rasmussen's invariant
• Concordance invariants from the $E(-1)$ spectral sequence on Khovanov homology
• Link Floer homology also detects split links
• A mixed invariant of non-orientable surfaces in equivariant Khovanov homology
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• Categorical lifting of the Jones polynomial: a survey
• Links of Second Smallest Knot Floer Homology
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• A family of slice-torus invariants from the divisibility of Lee classes
• Twisted Alexander invariants detect trivial links
• Dehn surgery and non-separating two-spheres
• Earrings, sutures and pointed links
• HOMFLYPT Homology over ${\mathbb{Z}}_2$ Detects Unlinks
• Two detection results of Khovanov homology on links
• Non-Trivial Steenrod Squares on Prime, Hyperbolic and Satellite Knots
• Betti Numbers of the HOMFLYPT Homology
• sl(3) Khovanov module and the detection of the planar theta-graph