### Abstract

In [28], Lawrence Roberts, extending the work of Ozsva ́th and Szabo ́ in [22], showed how to associate to a link L in the complement of a fixed unknot B ⊂ S^{3} a spectral sequence whose E^{2} term is the Khovanov homology of a link in a thickened annulus defined by Asaeda, Przytycki and Sikora in [1], and whose E^{∞} term is the knot Floer homology of the preimage of B inside the double-branched cover of L. In [6], we extended [22] in a different direction, constructing for each knot K ⊂ S^{3} and each n n Ie{cyrillic, ukrainian} Z_{+}, a spectral sequence from Khovanov's categorification of the reduced, n-colored Jones polynomial to the sutured Floer homology of a reduced n-cable of K. In the present work, we reinterpret Roberts' result in the language of Juha ́sz's sutured Floer homology [8] and show that the spectral sequence of [6] is a direct summand of the spectral sequence of [28].

Original language | English (US) |
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Pages (from-to) | 2009-2039 |

Number of pages | 31 |

Journal | Algebraic and Geometric Topology |

Volume | 10 |

Issue number | 4 |

DOIs | |

State | Published - 2010 |

### ASJC Scopus subject areas

- Geometry and Topology

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## Cite this

*Algebraic and Geometric Topology*,

*10*(4), 2009-2039. https://doi.org/10.2140/agt.2010.10.2009