Symplectic Manifolds and Isomonodromic Deformations
Differential Geometry
2020-02-04 v1 Algebraic Geometry
Symplectic Geometry
Exactly Solvable and Integrable Systems
Abstract
We study moduli spaces of meromorphic connections (with arbitrary order poles) over Riemann surfaces together with the corresponding spaces of monodromy data (involving Stokes matrices). Natural symplectic structures are found and described both explicitly and from an infinite dimensional viewpoint (generalising the Atiyah-Bott approach). This enables us to give an intrinsic symplectic description of the isomonodromic deformation equations of Jimbo, Miwa and Ueno, thereby putting the existing results for the six Painleve equations and Schlesinger's equations into a uniform framework.
Cite
@article{arxiv.2002.00052,
title = {Symplectic Manifolds and Isomonodromic Deformations},
author = {Philip Boalch},
journal= {arXiv preprint arXiv:2002.00052},
year = {2020}
}
Comments
Published in 2001 (based on part of 1999 Oxford thesis), posted here for easier accessibility