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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Khovanov module and the detection of unlinks

Matthew Hedden and Yi Ni

Geometry & Topology 17 (2013) 3027–3076
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 ΛH1–module structure on Heegaard Floer homology detects S1 × S2 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/