Algebraic & Geometric Topology 5 (2005) 1389–1418

DOI: 10.2140/agt.2005.5.1389

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 K_L is obtained.

Keywords

Floer homology, knot, longitude, Whitehead double

Mathematical Subject Classification

Primary: 57R58

Secondary: 57M25, 57M27

References

Publication

Received: 15 July 2004
Accepted: 8 July 2005
Published: 15 October 2005

Authors