An explicit algorithm realizes homologically nontrivial curves as Legendrian on ribbon surfaces of Legendrian graphs and converts abstract open books into contact surgery diagrams, with a uniqueness result for such realizations.
Surgery diagrams and open book decompositions of contact 3-manifolds
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An algorithm to Legendrian realize a curve on a ribbon surface
An explicit algorithm realizes homologically nontrivial curves as Legendrian on ribbon surfaces of Legendrian graphs and converts abstract open books into contact surgery diagrams, with a uniqueness result for such realizations.