  We introduce left central and right central functions and left and right
leaves in quasi-Poisson geometry, generalizing central (or Casimir) functions
and symplectic leaves from Poisson geometry. They lead to a new type of
(quasi-)Poisson reduction, which is both simpler and more general than known
quasi-Hamiltonian reductions. We study these notions in detail for moduli
spaces of flat connections on surfaces, where the quasi-Poisson structure is
given by an intersection pairing on homology.
