Volume 5, issue 4 (2005)

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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 $K\subset {S}^{3}$ 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 $\left(2,2n+1\right)$ torus knots. Finally a correspondence between the longitude Floer homology of $K$ and the Ozsváth–Szabó Floer homology of its Whitehead double ${K}_{L}$ is obtained.

Keywords
Floer homology, knot, longitude, Whitehead double
Mathematical Subject Classification 2000
Primary: 57R58
Secondary: 57M25, 57M27