Abstract

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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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1151-1169
Launched on MUSE
2008-10-06
Open Access
No
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