# Knot Floer homology detects genus-one fibred knots

@article{Ghiggini2006KnotFH,
title={Knot Floer homology detects genus-one fibred knots},
author={Paolo Ghiggini},
journal={American Journal of Mathematics},
year={2006},
volume={130},
pages={1151 - 1169}
}
• P. Ghiggini
• Published 18 March 2006
• Mathematics
• American Journal of Mathematics
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.
164 Citations

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