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arXiv · 2505.16689

Deformations of quasi-Hamiltonian spaces

Jean-Philippe Burelle·Mohamed Moussadek Maiza·Maxence Mayrand
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Abstract

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 $G \times G$ of a Lie group, viewed as a quasi-Hamiltonian $G \times G$-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 $T^*G^{r+g}$.

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Jean-Philippe Burelle, Mohamed Moussadek Maiza, Maxence Mayrand. 2025-05-22. Deformations of quasi-Hamiltonian spaces. https://doi.org/10.1016/j.difgeo.2026.102371

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