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A
note on the knot Floer homology of fibered knots
John A Baldwin and David Shea Vela-Vick |
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Algebraic & Geometric Topology 18 (2018) 3669–3690
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Abstract |
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We prove that the knot Floer homology of a fibered knot is nontrivial in its next-to-top Alexander grading. Immediate applications include new proofs of Krcatovich’s result that knots with –space surgeries are prime and Hedden and Watson’s result that the rank of knot Floer homology detects the trefoil among knots in the –sphere. We also generalize the latter result, proving a similar theorem for nullhomologous knots in any –manifold. We note that our method of proof inspired Baldwin and Sivek’s recent proof that Khovanov homology detects the trefoil. As part of this work, we also introduce a numerical refinement of the Ozsváth–Szabó contact invariant. This refinement was the inspiration for Hubbard and Saltz’s annular refinement of Plamenevskaya’s transverse link invariant in Khovanov homology. |
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Keywords
open book, transverse braid, Heegaard Floer homology
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Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R17, 57R58
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References |
Publication
Received: 19 January 2018
Revised: 6 July 2018
Accepted: 17 July 2018
Published: 18 October 2018
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Authors |
| John A Baldwin | |
| Department of Mathematics Boston College Chestnut Hill, MA United States |
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| https://www2.bc.edu/john-baldwin/ | |
| David Shea Vela-Vick | |
| Department of Mathematics Louisiana State University Baton Rouge, LA United States |
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| http://www.math.lsu.edu/~shea | |
