Inequivalent contact structures on Boothby-Wang 5-manifolds

TL;DR

This paper explores contact structures on certain 5-manifolds, linking contact homology invariants to symplectic geometry, and presents new inequivalent contact structures with specific topological properties.

Contribution

It establishes a relationship between contact homology invariants and the divisibility of the canonical class in symplectic 4-manifolds, and constructs new inequivalent contact structures.

Findings

Contact homology invariants relate to the canonical class divisibility.

New inequivalent contact structures found on Boothby-Wang 5-manifolds.

Examples with non-zero first Chern class are provided.

Abstract

We consider contact structures on simply-connected 5-manifolds which arise as circle bundles over simply-connected symplectic 4-manifolds and show that invariants from contact homology are related to the divisibility of the canonical class of the symplectic structure. As an application we find new examples of inequivalent contact structures in the same equivalence class of almost contact structures with non-zero first Chern class.