Deformations of quasi-Hamiltonian spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908922336509952 |
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| author | Burelle, Jean-Philippe Maiza, Mohamed Moussadek Mayrand, Maxence |
| author_facet | Burelle, Jean-Philippe Maiza, Mohamed Moussadek Mayrand, Maxence |
| contents | 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 $T^*G^{r+g}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_16689 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deformations of quasi-Hamiltonian spaces Burelle, Jean-Philippe Maiza, Mohamed Moussadek Mayrand, Maxence Symplectic Geometry Differential Geometry 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 $T^*G^{r+g}$. |
| title | Deformations of quasi-Hamiltonian spaces |
| topic | Symplectic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2505.16689 |