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2010 Manifolds with small Heegaard Floer ranks
Matthew Hedden, Yi Ni
Geom. Topol. 14(3): 1479-1501 (2010). DOI: 10.2140/gt.2010.14.1479

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.

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Matthew Hedden. Yi Ni. "Manifolds with small Heegaard Floer ranks." Geom. Topol. 14 (3) 1479 - 1501, 2010. https://doi.org/10.2140/gt.2010.14.1479

Information

Received: 11 August 2009; Revised: 26 May 2010; Accepted: 24 February 2010; Published: 2010
First available in Project Euclid: 20 December 2017

zbMATH: 1206.57014
MathSciNet: MR2653731
Digital Object Identifier: 10.2140/gt.2010.14.1479

Subjects:
Primary: 57M27
Secondary: 57M25

Rights: Copyright © 2010 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2010
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