Longitude Floer homology and the Whitehead double

Details Longitude Floer homology and the Whitehead double Longitude Floer homology and the Whitehead double

2004-07-13

arxiv.org/abs/math/0407211v4

Algebr. Geom. Topol. 5 (2005) 1389-1418

Mathematics

Geometric Topology

Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol5/agt-5-54.abs.html

Scientific paper

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.

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