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, Yp,q, discovered by physicists by showing that Yp,q and Yp',q' are inequivalent as contact structures if and only if p≠p'.