Longitude Floer homology and the Whitehead double

Eftekhary, Eaman

doi:10.2140/agt.2005.5.1389

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Longitude Floer homology and the Whitehead double

Eaman Eftekhary

Algebraic & Geometric Topology 5 (2005) 1389–1418

DOI: 10.2140/agt.2005.5.1389

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 $(2, 2 n + 1)$ 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

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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

Volume 5, issue 4 (2005)