Two contact surgery diagrams represent contactomorphic manifolds if and only if they are related by planar isotopies, Legendrian Reidemeister moves, cancelling pairs, handle slides, lantern moves, and chain moves.
Topological methods in 3-dimensional contact geometry
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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.
citing papers explorer
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A contact version of Kirby's theorem
Two contact surgery diagrams represent contactomorphic manifolds if and only if they are related by planar isotopies, Legendrian Reidemeister moves, cancelling pairs, handle slides, lantern moves, and chain moves.
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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.