Volume 10, issue 4 (2010)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Subscriptions
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Author Index
To Appear
ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 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 +, 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
References
Publication
Received: 20 August 2009
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