Knot Floer homology detects genus-one fibred knots
Knot Floer homology detects genus-one fibred knots
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Knot Floer 同源性检测属一纤维结
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发表时间：
2006
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通讯作者：
P. Ghiggini
中科院分区：
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作者：
P. Ghiggini
Ozsv‘ath和Szab’o猜想纽结Floer同调检测纤维纽结.我们基于接触拓扑学和Gabai的缝合流形分解理论提出了一种策略来逼近这一猜想.我们对亏格1的纽结实现了这一策略，作为推论，如果对纽结进行有理运算$K$得到Poincar同调球面$Sigma(2，3，5)$，则$K$是左手树形纽结.
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.