Volume 5, issue 4 (2005)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Longitude Floer homology and the Whitehead double

Eaman Eftekhary

Algebraic & Geometric Topology 5 (2005) 1389–1418

arXiv: math.GT/0407211

Abstract

We define the longitude Floer homology of a knot K S3 and show that it is a topological invariant of K. Some basic properties of these homology groups are derived. In particular, we show that they distinguish the genus of K. We also make explicit computations for the (2,2n + 1) torus knots. Finally a correspondence between the longitude Floer homology of K and the Ozsváth–Szabó Floer homology of its Whitehead double KL is obtained.

Keywords
Floer homology, knot, longitude, Whitehead double
Mathematical Subject Classification 2000
Primary: 57R58
Secondary: 57M25, 57M27
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Publication
Received: 15 July 2004
Accepted: 8 July 2005
Published: 15 October 2005
Authors
Eaman Eftekhary
Mathematics Department
Harvard University
1 Oxford Street
Cambridge MA 02138
USA