TY - JOUR

T1 - Khovanov homology, sutured floer homology and annular links

AU - Elisenda Grigsby, J.

AU - Wehrli, Stephan M.

PY - 2010

Y1 - 2010

N2 - 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 ⊂ 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 [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 ⊂ S3 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].

AB - 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 ⊂ 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 [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 ⊂ S3 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].

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U2 - 10.2140/agt.2010.10.2009

DO - 10.2140/agt.2010.10.2009

M3 - Article

AN - SCOPUS:78650566829

SN - 1472-2747

VL - 10

SP - 2009

EP - 2039

JO - Algebraic and Geometric Topology

JF - Algebraic and Geometric Topology

IS - 4

ER -