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15 August 2007 Quasi-Hamiltonian geometry of meromorphic connections
Philip Boalch
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Duke Math. J. 139(2): 369-405 (15 August 2007). DOI: 10.1215/S0012-7094-07-13924-3

Abstract

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

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Philip Boalch. "Quasi-Hamiltonian geometry of meromorphic connections." Duke Math. J. 139 (2) 369 - 405, 15 August 2007. https://doi.org/10.1215/S0012-7094-07-13924-3

Information

Published: 15 August 2007
First available in Project Euclid: 31 July 2007

zbMATH: 1126.53055
MathSciNet: MR2352135
Digital Object Identifier: 10.1215/S0012-7094-07-13924-3

Subjects:
Primary: 34M40, 53D30
Secondary: 22E67

Rights: Copyright © 2007 Duke University Press

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Vol.139 • No. 2 • 15 August 2007
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