Khovanov module and the detection of unlinks

Creators: Hedden, Matthew; Ni, Yi

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 × S^2 connected summands.

Additional Information

© 2013 Mathematical Sciences Publishers. Received: 6 May 2013; Accepted: 15 June 2013; Published: 17 October 2013. This work was initiated when the authors participated the "Homology Theories of Knots and Links" program at MSRI, and was carried out further when the authors visited the Simons Center for Geometry and Physics. We are grateful to Ciprian Manolescu and Tomasz Mrowka for helpful conversations. We also wish to thank Robert Lipshitz, Sucharit Sarkar and the referee for pointing out a mistake in the proof of Proposition 2.2. Special thanks are due to Sucharit Sarkar for suggesting a way to fix the mistake. The first author was partially supported by NSF grant numbers DMS-0906258 and DMS-1150872 and an Alfred P Sloan Research Fellowship. The second author was partially supported by an AIM Five-Year Fellowship, NSF grant numbers DMS-1021956, DMS-1103976 and an Alfred P Sloan Research Fellowship.

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