Volume 5, issue 3 (2005)

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
On knot Floer homology and cabling

Matthew Hedden

Algebraic & Geometric Topology 5 (2005) 1197–1222

arXiv: math.GT/0406402

Abstract

This paper is devoted to the study of the knot Floer homology groups HFK̂(S3,K2,n), where K2,n denotes the (2,n) cable of an arbitrary knot, K. It is shown that for sufficiently large |n|, the Floer homology of the cabled knot depends only on the filtered chain homotopy type of CFK̂(K). A precise formula for this relationship is presented. In fact, the homology groups in the top 2 filtration dimensions for the cabled knot are isomorphic to the original knot’s Floer homology group in the top filtration dimension. The results are extended to (p,pn ± 1) cables. As an example we compute HFK̂((T2,2m+1)2,2n+1) for all sufficiently large |n|, where T2,2m+1 denotes the (2,2m + 1)–torus knot.

Keywords
knots, Floer homology, cable, satellite, Heegaard diagrams
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57R58
References
Forward citations
Publication
Received: 9 August 2004
Revised: 23 July 2005
Accepted: 14 March 2005
Published: 20 September 2005
Authors
Matthew Hedden
Department of Mathematics
Princeton University
Princeton NJ 08544-1000
USA