Khovanov homology, sutured Floer homology and annular links

Grigsby, J Elisenda¹ ; Wehrli, Stephan M²

¹Mathematics Department, Boston College, 301 Carney Hall, Chestnut Hill MA 02467
²Mathematics Department, Syracuse University, 215 Carnegie, Syracuse NY 13244

Algebraic and Geometric Topology, Tome 10 (2010) no. 4, pp. 2009-2039

Résumé

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 L in the complement of a fixed unknotB ⊂ S3 a spectral sequence whose E2 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∞ term is the knot Floer homology of the preimage of B inside the double-branched cover of L.

In [Adv. Math. 223 (2010) 2114-2165], we extended the aforementioned Ozsváth–Szabó paper in a different direction, constructing for each knot K ⊂ S3 and each n ∈ 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.

Détail

DOI : 10.2140/agt.2010.10.2009

Keywords: Heegaard Floer homology, Khovanov homology, link invariants, branched covers

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