Volume 14, issue 3 (2010)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Manifolds with small Heegaard Floer ranks

Matthew Hedden and Yi Ni

Geometry & Topology 14 (2010) 1479–1501
Abstract

We show that the only irreducible three-manifold with positive first Betti number and Heegaard Floer homology of rank two is homeomorphic to zero-framed surgery on the trefoil. We classify links whose branched double cover gives rise to this manifold. Together with a spectral sequence from Khovanov homology to the Floer homology of the branched double cover, our results show that Khovanov homology detects the unknot if and only if it detects the two component unlink.

Keywords
Heegaard Floer homology, Khovanov homology, two-component unlink, torus bundle
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M25
References
Publication
Received: 11 August 2009
Revised: 26 May 2010
Accepted: 24 February 2010
Published: 11 June 2010
Proposed: Ron Fintushel
Seconded: Peter Ozsváth, Ron Stern
Authors
Matthew Hedden
Department of Mathematics
Michigan State University
East Lansing, MI 48824
http://www.math.msu.edu/~mhedden/Site/Home.html
Yi Ni
Department of Mathematics
Caltech
Pasadena, CA 91125
http://www.its.caltech.edu/~yini/