TL;DR
This paper extends Giroux's theorem by demonstrating that contact structures on closed 3-manifolds can be supported by open book decompositions with pages solving a homologically perturbed holomorphic curve equation.
Contribution
It introduces a novel method to select open book decompositions with pages satisfying a homologically perturbed holomorphic curve equation, expanding the understanding of contact structures.
Findings
Open book decompositions can be chosen with pages solving a perturbed holomorphic curve equation.
Supports all contact structures on closed 3-manifolds.
Provides a new geometric approach to studying contact structures.
Abstract
Emmanuel Giroux showed that every contact structure on a closed three dimensional manifold is supported by an open book decomposition. We will extend this result by showing that the open book decomposition can be chosen in such a way that the pages are solutions to a homologically perturbed Holomorphic Curve equation.
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