Algebraic and Geometric Topology 5 (2005), paper no. 54, pages 1389-1418.

Longitude Floer homology and the Whitehead double

Eaman Eftekhary

Abstract. We define the longitude Floer homology of a knot K in S^3 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 Ozsvath-Szabo Floer homology of its Whitehead double K_L is obtained.

Keywords. Floer homology, knot, longitude, Whitehead double

AMS subject classification. Primary: 57R58. Secondary: 57M25, 57M27.

E-print: arXiv:math.GT/0407211

DOI: 10.2140/agt.2005.5.1389

Submitted: 15 July 2004. Accepted: 8 July 2005. Published: 15 October 2005.

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Eaman Eftekhary
Mathematics Department, Harvard University
1 Oxford Street, Cambridge, MA 02138, USA

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