Contact structures on M \times S^2

TL;DR

This paper proves that if a manifold M has a contact structure, then the product M×S^2 also admits a contact structure, extending known results through surgery theory and contact surgery theorems.

Contribution

It establishes the existence of contact structures on M×S^2 whenever M admits one, using advanced surgical techniques and existing theorems.

Findings

Contact structures on M imply contact structures on M×S^2.

Utilizes surgery theory and Eliashberg's contact surgery theorem.

Builds on Bourgeois's result for M×T^2.

Abstract

We show that if a manifold M admits a contact structure, then so does M\times S^2. Our proof relies on surgery theory, a theorem of Eliashberg on contact surgery and a theorem of Bourgeois showing that if M admits a contact structure then so does M\times T^2.