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Quasi-Hamiltonian quotients as disjoint unions of symplectic manifolds

Florent Schaffhauser
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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.

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Florent Schaffhauser. 2008-06-16. Quasi-Hamiltonian quotients as disjoint unions of symplectic manifolds. https://doi.org/10.1142/9789812779649_0002

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