Knot Floer homology detects genus-one fibred knots

• Autores: P. Ghiggini
• Localización: American journal of mathematics, ISSN 0002-9327, Vol. 130, Nº 5, 2008, págs. 1151-1170
• Idioma: inglés
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• Resumen

  • 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.