Abstract
In this chapter, we consider the moduli space of flat connections on a (trivial) bundle over a surface (defined in § V.1). There is a Hamiltonian group action that allows us to endow this space with a Poisson structure, as we show in § V.2 (this is due to Atiyah and Bott [10] in the case of a closed surface and to Fock and Roslyi [50] in the general case of a surface with boundary). We then look at a special case in § V.3, in which there is an integrable system (due to Goldman [56]) on the moduli space. Following Jeffrey and Weitsman [77], we exhibit a torus action and its momentum mapping, that is, action-angle variables for this system.
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