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. 

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