#### Volume 18, issue 6 (2018)

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A note on the knot Floer homology of fibered knots

### John A Baldwin and David Shea Vela-Vick

Algebraic & Geometric Topology 18 (2018) 3669–3690
##### Abstract

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 $L$–space surgeries are prime and Hedden and Watson’s result that the rank of knot Floer homology detects the trefoil among knots in the $3$–sphere. We also generalize the latter result, proving a similar theorem for nullhomologous knots in any $3$–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
##### Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57R17, 57R58
##### Publication
Received: 19 January 2018
Revised: 6 July 2018
Accepted: 17 July 2018
Published: 18 October 2018
##### Authors
 John A Baldwin Department of Mathematics Boston College Chestnut Hill, MA United States https://www2.bc.edu/john-baldwin/ David Shea Vela-Vick Department of Mathematics Louisiana State University Baton Rouge, LA United States http://www.math.lsu.edu/~shea