Longitude Floer homology and the

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-Szabo ́ Floer homology of its Whitehead double KL is obtained. AMS Classification 57R58; 57M25, 57M2