Translator Disclaimer
2010 Khovanov homology, sutured Floer homology and annular links
J Elisenda Grigsby, Stephan M Wehrli
Algebr. Geom. Topol. 10(4): 2009-2039 (2010). DOI: 10.2140/agt.2010.10.2009

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 L in the complement of a fixed unknotBS3 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 KS3 and each n+, 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.

Citation

Download Citation

J Elisenda Grigsby. Stephan M Wehrli. "Khovanov homology, sutured Floer homology and annular links." Algebr. Geom. Topol. 10 (4) 2009 - 2039, 2010. https://doi.org/10.2140/agt.2010.10.2009

Information

Received: 20 August 2009; Accepted: 20 November 2009; Published: 2010
First available in Project Euclid: 19 December 2017

zbMATH: 1206.57012
MathSciNet: MR2728482
Digital Object Identifier: 10.2140/agt.2010.10.2009

Subjects:
Primary: 57M12, 57M27
Secondary: 57R58, 81R50

Rights: Copyright © 2010 Mathematical Sciences Publishers

JOURNAL ARTICLE
31 PAGES


SHARE
Vol.10 • No. 4 • 2010
MSP
Back to Top