## Algebraic & Geometric Topology

### Longitude Floer homology and the Whitehead double

Eaman Eftekhary

#### 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.

#### Article information

Source
Algebr. Geom. Topol., Volume 5, Number 4 (2005), 1389-1418.

Dates
Accepted: 8 July 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.agt/1513796481

Digital Object Identifier
doi:10.2140/agt.2005.5.1389

Mathematical Reviews number (MathSciNet)
MR2171814

Zentralblatt MATH identifier
1087.57021

#### Citation

Eftekhary, Eaman. Longitude Floer homology and the Whitehead double. Algebr. Geom. Topol. 5 (2005), no. 4, 1389--1418. doi:10.2140/agt.2005.5.1389. https://projecteuclid.org/euclid.agt/1513796481

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