Ghiggini, Paolo Knot Floer homology detects genus-one fibred knots. (English) Zbl 1149.57019 Am. J. Math. 130, No. 5, 1151-1169 (2008). Summary: Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots. We propose a strategy to approach this conjecture based on Gabai’s theory of sutured manifold decomposition and contact topology. We implement this strategy for genus-one knots and links, obtaining as a corollary that if rational surgery on a knot \(K\) gives the Poincaré homology sphere \(\Sigma(2, 3, 5)\), then \(K\) is the left-handed trefoil knot. Cited in 6 ReviewsCited in 86 Documents MSC: 57M27 Invariants of knots and \(3\)-manifolds (MSC2010) 57M25 Knots and links in the \(3\)-sphere (MSC2010) PDFBibTeX XMLCite \textit{P. Ghiggini}, Am. J. Math. 130, No. 5, 1151--1169 (2008; Zbl 1149.57019) Full Text: DOI arXiv