Geometry & Topology

Manifolds with small Heegaard Floer ranks

Matthew Hedden and Yi Ni

Full-text: Open access

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.

Article information

Source
Geom. Topol., Volume 14, Number 3 (2010), 1479-1501.

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

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513732230

Digital Object Identifier
doi:10.2140/gt.2010.14.1479

Mathematical Reviews number (MathSciNet)
MR2653731

Zentralblatt MATH identifier
1206.57014

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}

Keywords
Heegaard Floer homology Khovanov homology two-component unlink torus bundle

Citation

Hedden, Matthew; Ni, Yi. Manifolds with small Heegaard Floer ranks. Geom. Topol. 14 (2010), no. 3, 1479--1501. doi:10.2140/gt.2010.14.1479. https://projecteuclid.org/euclid.gt/1513732230


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