The Giroux correspondence in arbitrary dimensions

TL;DR

This paper extends the Giroux correspondence to all dimensions, providing new proofs and confirming conjectures related to Weinstein domains and Lefschetz fibrations in symplectic topology.

Contribution

It generalizes the Giroux correspondence to arbitrary dimensions and proves related conjectures about Weinstein structures and Lefschetz fibrations.

Findings

Established Giroux correspondence in all dimensions

Provided an alternative proof for Weinstein domain homotopy to Lefschetz fibrations

Confirmed moves relating Weinstein Lefschetz fibrations with homotopic Weinstein structures

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.