On the equivalence of Legendrian and transverse invariants in knot Floer homology
arXiv:1112.5970 · doi:10.2140/gt.2013.17.925
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.
41 pages, 29 figures
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- Functoriality of the EH class and the LOSS invariant under Lagrangian concordances
- Ozsváth-Szabó invariants of contact surgeries
- Quasi right-veering braids and non-loose links
- Rank Bounds in Link Floer Homology and Detection Results
- Braids and combinatorial knot Floer homology
- Transverse and Legendrian invariants of cables in combinatorial link Floer homology
- On contact surgery and knot Floer invariants
- Transverse braids and combinatorial knot Floer homology
- Invariants of annular links, cobordisms and transverse links from combinatorial link Floer complex
- A note on a Geography problem in knot Floer homology
- Transverse links, open books and overtwisted manifolds
- On the invariance of the Dowlin spectral sequence