Volume 6, issue 3 (2006)

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

Volume 18
Issue 4, 1883–2507
Issue 3, 1259–1881
Issue 2, 635–1258
Issue 1, 1–633

Volume 17, 6 issues

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