Introduction to moduli spaces and Dirac geometry
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910987364335616 |
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| author | Meinrenken, Eckhard |
| author_facet | Meinrenken, Eckhard |
| contents | Let $G$ be a Lie group, with an invariant metric on its Lie algebra $\mathfrak{g}$. Given a surface $Σ$ with boundary, and a collection of base points $\mathcal{V}\subset Σ$ meeting every boundary component, the moduli space (representation variety) $\mathcal{M}_G(Σ,\mathcal{V})$ carries a distinguished `quasi-symplectic' 2-form. We shall explain the finite-dimensional construction of this 2-form and discuss its basic properties, using quasi-Hamiltonian techniques and Dirac geometry. This article is an extended version of lectures given at the summer school 'Poisson 2024' at the Accademia Pontaniana in Napoli, July 2024. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04150 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Introduction to moduli spaces and Dirac geometry Meinrenken, Eckhard Differential Geometry Let $G$ be a Lie group, with an invariant metric on its Lie algebra $\mathfrak{g}$. Given a surface $Σ$ with boundary, and a collection of base points $\mathcal{V}\subset Σ$ meeting every boundary component, the moduli space (representation variety) $\mathcal{M}_G(Σ,\mathcal{V})$ carries a distinguished `quasi-symplectic' 2-form. We shall explain the finite-dimensional construction of this 2-form and discuss its basic properties, using quasi-Hamiltonian techniques and Dirac geometry. This article is an extended version of lectures given at the summer school 'Poisson 2024' at the Accademia Pontaniana in Napoli, July 2024. |
| title | Introduction to moduli spaces and Dirac geometry |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2506.04150 |