纽结 Floer 同调可检测亏格一纤维纽结
摘要
Ozsvath 与 Szabo 猜想纽结 Floer 同调可检测纤维纽结。我们基于 Gabai 的缝合流形分解理论与接触拓扑提出一种逼近该猜想的策略。我们对亏格一纽结实施了此策略，得到一个推论：若对纽结 进行有理手术得到 Poincaré 同调球面 ，则 为左手三叶纽结。
引用
@article{arxiv.math/0603445,
title = {Knot Floer homology detects genus-one fibred knots},
author = {Paolo Ghiggini},
journal= {arXiv preprint arXiv:math/0603445},
year = {2007}
}
备注
The paper used to be known as "Knot Floer homology detects fibred links", however there was a mistake in the proof of Theorem 1.9 concerning links. The result about knots (Theorem 1.4) and the application to surgeries giving the Poincare' homology sphere (Corollary 1.7), as well as the applications by Ozsvath and Szabo (math.GT/0604079) and Yi Ni (math.GT/0607156) are uneffected by the mistake. This version is essentially the previous one, without Theorem 1.9 and Subsection 4.3. A more revised version is going to appear on Amer. J. Math. and is available on my personal webpage at http://www.labmath.uqam.ca/~ghiggini/papers.html