Deformations of quasi-Hamiltonian spaces

We introduce a notion of deformations of quasi-Hamiltonian G -spaces to Hamiltonian G -spaces and provide several examples. In particular, we show that the double G × G of a Lie group, viewed as a quasi-Hamiltonian G × G -space, deforms smoothly to the cotangent bundle T ⁎ G . Likewise, any conjugacy class of G sufficiently close to the identity deforms to a coadjoint orbit. We further show that the moduli space of flat G -connections on a compact oriented surface of genus g with r + 1 boundary components deforms to T ⁎ G r + g .