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
References
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