Quasi-Hamiltonian quotients as disjoint unions of symplectic manifolds

Abstract

We show that the quotient associated to a quasi-Hamiltonian space has a symplectic structure even when 1 is not a regular value of the momentum map: it is a disjoint union of symplectic manifolds of possibly different dimensions, which generalizes a result of Alekseev, Malkin and Meinrenken. We illustrate this theorem with the example of representation spaces of surface groups. As an intermediary step, we show that the isotropy submanifolds of a quasi-Hamiltonian space are quasi-Hamiltonian spaces themselves.

References in corpus (2)

• Symplectic and Poisson structures of certain moduli spaces
• The real locus of an involution map on the moduli space of flat connections on a Riemann surface

Cited by in corpus (1)

• Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups