Algebraic & Geometric Topology

Longitude Floer homology and the Whitehead double

Eaman Eftekhary

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Abstract

We define the longitude Floer homology of a knot KS3 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
Received: 15 July 2004
Accepted: 8 July 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 57R58: Floer homology
Secondary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45} 57M27: Invariants of knots and 3-manifolds

Keywords
Floer homology knot longitude Whitehead double

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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References

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