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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 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
Baldwin, John 1 ; Vela-Vick, David 2
@article{10_2140_agt_2018_18_3669,
author = {Baldwin, John and Vela-Vick, David},
title = {A note on the knot {Floer} homology of fibered knots},
journal = {Algebraic and Geometric Topology},
pages = {3669--3690},
publisher = {mathdoc},
volume = {18},
number = {6},
year = {2018},
doi = {10.2140/agt.2018.18.3669},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3669/}
}
TY - JOUR AU - Baldwin, John AU - Vela-Vick, David TI - A note on the knot Floer homology of fibered knots JO - Algebraic and Geometric Topology PY - 2018 SP - 3669 EP - 3690 VL - 18 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3669/ DO - 10.2140/agt.2018.18.3669 ID - 10_2140_agt_2018_18_3669 ER -
%0 Journal Article %A Baldwin, John %A Vela-Vick, David %T A note on the knot Floer homology of fibered knots %J Algebraic and Geometric Topology %D 2018 %P 3669-3690 %V 18 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2018.18.3669/ %R 10.2140/agt.2018.18.3669 %F 10_2140_agt_2018_18_3669
Baldwin, John; Vela-Vick, David. A note on the knot Floer homology of fibered knots. Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3669-3690. doi: 10.2140/agt.2018.18.3669
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