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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.

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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.

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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.
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Princeton University Centennial FellowshipUNSPECIFIED
AIM Five-Year FellowshipUNSPECIFIED
Clay Mathematics InstituteUNSPECIFIED
Issue or Number:3
Classification Code:Mathematics Subject Classification (2000): 57R58, 57M27, 57R30
Record Number:CaltechAUTHORS:20150421-115906058
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:56827
Deposited By: George Porter
Deposited On:21 Apr 2015 20:08
Last Modified:03 Oct 2019 08:17

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