Quasi-Hamiltonian Geometry of Meromorphic Connections
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arXiv
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| Format: | Preprint |
| Published: |
2002
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| _version_ | 1866917325366624256 |
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| author | Boalch, Philip |
| author_facet | Boalch, Philip |
| contents | For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on principal G-bundles over a disc, and they generalise the conjugacy class example of Alekseev, Malkin and Meinrenken (which appears in the simple pole case). Using the `fusion product' in the theory this gives a finite dimensional construction of the natural symplectic structures on the spaces of monodromy/Stokes data of meromorphic connections over arbitrary genus Riemann surfaces, together with a new proof of the symplectic nature of isomonodromic deformations of such connections. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0203161 |
| institution | arXiv |
| publishDate | 2002 |
| record_format | arxiv |
| spellingShingle | Quasi-Hamiltonian Geometry of Meromorphic Connections Boalch, Philip Differential Geometry Symplectic Geometry For each connected complex reductive group G, we find a family of new examples of complex quasi-Hamiltonian G-spaces with G-valued moment maps. These spaces arise naturally as moduli spaces of (suitably framed) meromorphic connections on principal G-bundles over a disc, and they generalise the conjugacy class example of Alekseev, Malkin and Meinrenken (which appears in the simple pole case). Using the `fusion product' in the theory this gives a finite dimensional construction of the natural symplectic structures on the spaces of monodromy/Stokes data of meromorphic connections over arbitrary genus Riemann surfaces, together with a new proof of the symplectic nature of isomonodromic deformations of such connections. |
| title | Quasi-Hamiltonian Geometry of Meromorphic Connections |
| topic | Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/math/0203161 |