The Giroux correspondence in arbitrary dimensions
arXiv:2307.02317
Abstract
We establish the Giroux correspondence in arbitrary dimensions. As corollaries we (i) give an alternate proof of a result of Giroux-Pardon that states that any Weinstein domain is Weinstein homotopic to one which admits a Weinstein Lefschetz fibration and (ii) prove that any two Weinstein Lefschetz fibrations whose Weinstein domain structures are Weinstein homotopic are related by the Weinstein Lefschetz fibration moves, affirming a conjecture of Giroux-Pardon.
v2: 68 pages; added Remark 1.1.12, labels to some figures, and a missing case in Proposition 4.1.7 and proof of Theorem 3.1.1; statement of Lemma 4.2.1 strengthened and proof rewritten accordingly