Symplectic manifolds and isomonodromic deformations
type: Item
instance of: scholarly article
title: Symplectic manifolds and isomonodromic deformations
zbMATH Open document ID: 1001.53059
author: Philip Boalch
published in: Advances in Mathematics
publication date: 2002-05-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/2002.00052
review text: The author studies the moduli spaces of meromorphic connections with poles of arbitrary order over Riemann surfaces together with the corresponding spaces of monodromy data involving Stokes matrices. Generalizing the Atiyah-Bott approach [\textit{M. F. Atiyah} and \textit{R. Bott}, Phil. Trans. R. Soc. Lond. 308, 523-615 (1983; Zbl 0509.14014)], natural symplectic structures on extended spaces of singular connections are found and described both explicitly and from an infinite dimensional viewpoint. By the symplectic space construction an intrinsic symplectic description of the isomonodromic deformation equations of Jimbo, Miwa and Ueno is given and the existing results for the six Painlevé equations and Schlesinger's equations are put into a uniform framework.
reviewed by: Stanisław Janeczko
Mathematics Subject Classification ID: 53D20
Mathematics Subject Classification ID: 34M55
Mathematics Subject Classification ID: 53D30
zbMATH DE Number: 1703321
zbMATH Keywords: symplectic manifold
zbMATH Keywords: Kähler structures
zbMATH Keywords: meromorphic connections
zbMATH Keywords: monodromy map
MaRDI profile type: Publication
OpenAlex ID: W3099105597
arXiv ID: 2002.00052
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Symplectic manifolds and isomonodromic deformations (DOI)
DOI: 10.1006/AIMA.2001.1998