Volume 18, issue 6 (2018)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
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.

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