Volume 6, issue 3 (2006)

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
Knot Floer homology in cyclic branched covers

J Elisenda Grigsby

Algebraic & Geometric Topology 6 (2006) 1355–1398

arXiv: math.GT/0507498

Abstract

In this paper, we introduce a sequence of invariants of a knot K in S3: the knot Floer homology groups HFK̂(Σm(K);K˜,i) of the preimage of K in the m–fold cyclic branched cover over K. We exhibit HFK̂(Σm(K);K˜,i) as the categorification of a well-defined multiple of the Turaev torsion of Σm(K) K˜ in the case where Σm(K) is a rational homology sphere. In addition, when K is a two-bridge knot, we prove that HFK̂(Σ2(K);K˜,s0)HFK̂(S3;K) for s0 the spin Spinc structure on Σ2(K). We conclude with a calculation involving two knots with identical HFK̂(S3;K,i) for which HFK̂(Σ2(K);K˜,i) differ as 2–graded groups.

Keywords
Heegaard Floer homology, branched covers
Mathematical Subject Classification 2000
Primary: 57R58, 57M27
Secondary: 57M05
References
Forward citations
Publication
Received: 9 September 2005
Accepted: 10 June 2006
Published: 25 September 2006
Authors
J Elisenda Grigsby
Evans Hall
University of California, Berkeley
Berkeley, CA 94720
USA