Completely integrable contact hamiltonian systems and toric contact structures on S2 × S3

Abstract

I begin by giving a general discussion of completely integrable Hamiltonian systems in the setting of contact geometry. We then pass to the particular case of toric contact structures on the manifold S2×S3. In particular we give a complete solution to the contact equivalence problem for a class of toric contact structures, Y p,q, discovered by physicists by showing that Y p,q and Y p′,q′ are inequivalent as contact structures if and only if p ≠ p′.