Knot Floer homology detects genus-one fibred knots

Details Knot Floer homology detects genus-one fibred knots Knot Floer homology detects genus-one fibred knots

2006-03-18

arxiv.org/abs/math/0603445v3

Mathematics

Geometric Topology

The paper used to be known as "Knot Floer homology detects fibred links", however there was a mistake in the proof of Theorem

Scientific paper

Ozsvath and Szabo conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on Gabai's theory of sutured manifold decomposition and contact topology. We implement this strategy for genus-one knots, obtaining as a corollary that, if rational surgery on a knot $K$ gives the Poincare homology sphere $\Sigma(2,3,5)$, then $K$ is the left-handed trefoil knot.

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