On the equivalence of Legendrian and transverse invariants in knot Floer homology

2011/12/27 by John A. Baldwin, David Shea Vela-Vick, Vera Vertesi · 1 citation
Mathematics · #math.SG #math.GT #msc:57M27 #msc:57R58

paper · pdf · doi:10.2140/gt.2013.17.925

published as Geom. Topol. 17 (2013) 925-974 · 41 pages, 29 figures

arxiv created 2011/12/27 · arxiv updated 2014/11/11

Abstract

Using the grid diagram formulation of knot Floer homology, Ozsvath, Szabo and Thurston defined an invariant of transverse knots in the tight contact 3-sphere. Shortly afterwards, Lisca, Ozsvath, Stipsicz and Szabo defined an invariant of transverse knots in arbitrary contact 3-manifolds using open book decompositions. It has been conjectured that these invariants agree where they are both defined. We prove this fact by defining yet another invariant of transverse knots, showing that this third invariant agrees with the two mentioned above.

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• The next-to-top term of the knot Floer homology of some non-fibered knots

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