A theorem gives sufficient conditions for an integrable system to descend through Poisson reduction, with explicit generalized action variables, applied to moduli spaces of flat connections and to the three doubles of compact Lie groups.
Torus Actions and Integrable Systems
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abstract
This is a survey on natural local torus actions which arise in integrable dynamical systems, and their relations with other subjects, including: reduced integrability, local normal forms, affine structures, monodromy, global invariants, integrable surgery, convexity properties of momentum maps, localization formulas, integrable PDEs.
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Integrable systems from Poisson reductions of generalized Hamiltonian torus actions
A theorem gives sufficient conditions for an integrable system to descend through Poisson reduction, with explicit generalized action variables, applied to moduli spaces of flat connections and to the three doubles of compact Lie groups.