Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$

Details Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$ Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$

2011-01-28

arxiv.org/abs/1101.5587v3

SIGMA 7 (2011), 058

Mathematics

Symplectic Geometry

based on a talk given at the S4 Conference in honor or Willard Miller, Jr

Scientific paper

10.3842/SIGMA.2011.058

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 $S^2\times S^3$. 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 $p\neq p'$.

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