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Knot Floer homology detects genus-one fibred knots
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 130, Number 5, October 2008
- pp. 1151-1169
- 10.1353/ajm.0.0016
- Article
- Additional Information
Ozsv\'ath and Szab\'o conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on contact topology and Gabai's theory of sutured manifold decomposition. We implement this strategy for genus-one knots, obtaining as a corollary that if rational surgery on a knot $K$ gives the Poincar\'e homology sphere $\Sigma(2,3,5)$, then $K$ is the left-handed trefoil knot.