Stable Hamiltonian structures in dimension three are supported by open books

TL;DR

This paper proves that all stable Hamiltonian structures on closed three-manifolds can be homotoped to be supported by open books, linking Hamiltonian dynamics with topological open book decompositions.

Contribution

It establishes a universal support theorem for stable Hamiltonian structures in dimension three, connecting them to open book decompositions.

Findings

Every stable Hamiltonian structure on a closed 3-manifold is supported by an open book.

Supports the homotopy equivalence between Hamiltonian structures and open book decompositions.

Provides a topological framework for understanding Hamiltonian dynamics in three dimensions.

Abstract

We prove that every stable Hamiltonian structure on a closed oriented three-manifold is stably homotopic to one which is supported (with suitable signs) by an open book.