Quasi-Hamiltonian geometry of meromorphic connections

By P. Boalch. 2002

111 citations recorded by the source corpus.

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 disk, and they generalise the conjugacy class example of Alekseev, Malkin, and Meinrenken [3] (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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/ee886f451f0f502ebd9e5cdf612aca84e1cfc6f4

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In Geometry and Topology

1. P. Boalch
2. Daisuke Yamakawa
3. O. Biquard
4. T. Mochizuki
5. Dan Xie
6. David Dumas
7. Michael Wolf
8. E. Witten

In Mathematical Physics

1. P. Boalch
2. Daisuke Yamakawa
3. O. Biquard
4. T. Mochizuki
5. Dan Xie
6. Carlos Simpson
7. David Dumas
8. Michael Wolf

Citations in the corpus

• Geometry of Multiplicative Preprojective Algebra (2007, unknown): “[3] Boalch, P. “Stokes matrices, Poisson Lie groups and Frobenius manifolds.””
• Wild non-abelian Hodge theory on curves (2001, background): “envalues of the residues, all integrable connections are stable, and the moduli space can be identified, from the complex symplectic viewpoint, with the finite dimensional quasi-Hamiltonian quotient of [Boa]. For example over the projective line the moduli space contains a dense opensubset, parameteri”
• Twisted wild character varieties (2015, background): “Note that Li-Bland–Severa [33] recently suggested a different approach to some of the results of [12, 14, 16], although not incorporating the new braiding.”
• Riemann–Hilbert for tame complex parahoric connections (2010, methodology): “In the first instance the 2-form ω was arrived at by actually computing what arose from the Hamiltonian loop group spaces related to resonant logarithmic connections on a disk, similarly to Section 4 of [8].”
• Geometry and braiding of Stokes data; Fission and wild character varieties (2011, methodology): “(It is symplectic if H is a maximal torus as in [15]).”