#### Volume 10, issue 4 (2010)

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Khovanov homology, sutured Floer homology and annular links

### J Elisenda Grigsby and Stephan M Wehrli

Algebraic & Geometric Topology 10 (2010) 2009–2039
##### Abstract

In [arXiv:0706.0741], Lawrence Roberts, extending the work of Ozsváth and Szabó in [Adv. Math 194 (2005) 1-33], showed how to associate to a link $\mathbb{L}$ in the complement of a fixed unknot$B\subset {S}^{3}$ 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 [Algebr. Geom. Topol. 4 (2004) 1177-1210], and whose ${E}^{\infty }$ term is the knot Floer homology of the preimage of $B$ inside the double-branched cover of $\mathbb{L}$.

In [Adv. Math. 223 (2010) 2114-2165], we extended the aforementioned Ozsváth–Szabó paper in a different direction, constructing for each knot $K\subset {S}^{3}$ and each $n\in {ℤ}_{+}$, 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 Juhasz’s sutured Floer homology [Algebr. Geom. Topol. 6 (2006) 1429–1457] and show that the spectral sequence of [Adv. Math. 223 (2010) 2114-2165] is a direct summand of the spectral sequence of Roberts’ paper.

##### Keywords
Heegaard Floer homology, Khovanov homology, link invariants, branched covers
##### Mathematical Subject Classification 2000
Primary: 57M12, 57M27
Secondary: 57R58, 81R50
##### Publication
Accepted: 20 November 2009
Published: 30 September 2010
##### Authors
 J Elisenda Grigsby Mathematics Department Boston College 301 Carney Hall Chestnut Hill MA 02467 http://www2.bc.edu/~grigsbyj/ Stephan M Wehrli Mathematics Department Syracuse University 215 Carnegie Syracuse NY 13244