Knot Floer homology detects fibred knots

Ni, Yi (2007) Knot Floer homology detects fibred knots. Inventiones Mathematicae, 170 (3). pp. 577-608. ISSN 0020-9910. https://resolver.caltech.edu/CaltechAUTHORS:20150421-115906058

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Abstract

Ozsváth and Szabó conjectured that knot Floer homology detects fibred knots in S^3. We will prove this conjecture for null-homologous knots in arbitrary closed 3-manifolds. Namely, if K is a knot in a closed 3-manifold Y, Y-K is irreducible, and \hat{HFK}(Y,K) is monic, then K is fibred. The proof relies on previous works due to Gabai, Ozsváth–Szabó, Ghiggini and the author. A corollary is that if a knot in S^3 admits a lens space surgery, then the knot is fibred.

Item Type:

Article

Related URLs:

URL	URL Type	Description
http://arxiv.org/abs/math/0607156	arXiv	Discussion Paper
http://dx.doi.org/10.1007/s00222-007-0075-9	DOI	Article
http://link.springer.com/article/10.1007/s00222-007-0075-9	Publisher	Article
http://arxiv.org/abs/0808.0940	arXiv	Erratum
http://dx.doi.org/10.1007/s00222-009-0174-x	DOI	Erratum
http://link.springer.com/article/10.1007/s00222-009-0174-x	Publisher	Erratum

Additional Information:

© 2007 Springer. Published online: 20 September 2007. Dedicated to Professor Boju Jiang on the occasion of his 70th birthday. This paper has been submitted to Princeton University as the author’s PhD thesis. We wish to thank David Gabai and Zoltán Szabó for their guidance. We would like to thank Paolo Ghiggini for many fruitful discussions during the course of this work. This paper benefits a lot from his work [5]. A version of Theorem 6.2 was also proved by Ian Agol via a different approach. We wish to thank him for some interesting discussions. We are grateful to Matthew Hedden, András Juhász, Tao Li, Peter Ozsváth, Jiajun Wang and Chenyang Xu for some helpful conversations and their interests in this work. We are particularly grateful to an anonymous referee for enormous suggestions and corrections. The author was partially supported by a Graduate School Centennial Fellowship at Princeton University. Parts of the work were carried out when the author visited UQAM and Peking University; he wishes to thank Steve Boyer, Olivier Collin and Shicheng Wang for their hospitality. The author extends his gratitude to the American Institute of Mathematics and the Clay Mathematics Institute for their subsequent support.

Funders:

Funding Agency	Grant Number
Princeton University Centennial Fellowship	UNSPECIFIED
AIM Five-Year Fellowship	UNSPECIFIED
Clay Mathematics Institute	UNSPECIFIED

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Classification Code:

Mathematics Subject Classification (2000): 57R58, 57M27, 57R30

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CaltechAUTHORS:20150421-115906058

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https://resolver.caltech.edu/CaltechAUTHORS:20150421-115906058

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56827

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CaltechAUTHORS

Deposited By:

George Porter

Deposited On:

21 Apr 2015 20:08

Last Modified:

03 Oct 2019 08:17

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