Khovanov module and the detection of unlinks

Hedden, Matthew; Ni, Yi

doi:10.2140/gt.2013.17.3027

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Khovanov module and the detection of unlinks

Matthew Hedden and Yi Ni

Geometry & Topology 17 (2013) 3027–3076

DOI: 10.2140/gt.2013.17.3027

Abstract

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 $Λ^{*} H_{1}$ –module structure on Heegaard Floer homology detects $S^{1} \times S^{2}$ connected summands.

Keywords

Khovanov module, Heegaard Floer homology, unlinks, branched double cover

Mathematical Subject Classification 2010

Primary: 57M27

Secondary: 57M25

References

Publication

Received: 6 May 2013

Accepted: 15 June 2013

Published: 17 October 2013

Proposed: Ronald Fintushel

Seconded: Robion Kirby, Ronald Stern

Authors

Matthew Hedden
Department of Mathematics Michigan State University A338 WH East Lansing, MI 48824 USA
http://www.math.msu.edu/~mhedden/Home.html
Yi Ni
Department of Mathematics California Institute of Technology 1200 E California Blvd Pasadena, CA 91125 USA
http://www.its.caltech.edu/~yini/

Volume 17, issue 5 (2013)