Algebraic and Geometric Topology 5 (2005),
paper no. 54, pages 1389-1418.
Longitude Floer homology and the Whitehead double
We define the longitude Floer homology of a knot K in 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
(2,2n+1) torus knots. Finally a correspondence between the longitude
Floer homology of K and the Ozsvath-Szabo Floer homology of its
Whitehead double K_L is obtained.
Floer homology, knot, longitude, Whitehead double
AMS subject classification.
Secondary: 57M25, 57M27.
Submitted: 15 July 2004.
Accepted: 8 July 2005.
Published: 15 October 2005.
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