Khovanov module and the detection of unlinks

Hedden, Matthew¹ ; Ni, Yi²

¹ Department of Mathematics, Michigan State University, A338 WH, East Lansing, MI 48824, USA
² Department of Mathematics, California Institute of Technology, 1200 E California Blvd, Pasadena, CA 91125, USA

Geometry & topology, Tome 17 (2013) no. 5, pp. 3027-3076.

Résumé

We study a module structure on Khovanov homology, which we show is natural under the Ozsváth–Szabó 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 ${\Lambda }^{\ast }{H}_1$–module structure on Heegaard Floer homology detects $S^1\times S^2$ connected summands.

Détail

DOI : 10.2140/gt.2013.17.3027

Classification : 57M27, 57M25
Keywords: Khovanov module, Heegaard Floer homology, unlinks, branched double cover

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