Symplectic Manifolds and Isomonodromic Deformations
Copyright policy )Symplectic Manifolds and Isomonodromic Deformations
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.
Published in 2001 (based on part of 1999 Oxford thesis), posted here for easier accessibility
- University of Paris France
- Institut de Mathématiques de Jussieu France
- Sorbonne University France
- UNIVERSITE PARIS DESCARTES France
- French National Centre for Scientific Research France
Mathematics - Differential Geometry, Mathematics(all), [NLIN.NLIN-SI] Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI], FOS: Physical sciences, Stokes matrices, Painlevé equations, [MATH] Mathematics [math], Kähler structures, Mathematics - Algebraic Geometry, symplectic manifold, Momentum maps; symplectic reduction, FOS: Mathematics, Algebraic Geometry (math.AG), meromorphic connections, Nonlinear Sciences - Exactly Solvable and Integrable Systems, monodromy map, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], [MATH.MATH-SG] Mathematics [math]/Symplectic Geometry [math.SG], gauge theory, Differential Geometry (math.DG), symplectic structure, Mathematics - Symplectic Geometry, Symplectic structures of moduli spaces, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Symplectic Geometry (math.SG), isomonodromic deformations, Exactly Solvable and Integrable Systems (nlin.SI), [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
Mathematics - Differential Geometry, Mathematics(all), [NLIN.NLIN-SI] Nonlinear Sciences [physics]/Exactly Solvable and Integrable Systems [nlin.SI], FOS: Physical sciences, Stokes matrices, Painlevé equations, [MATH] Mathematics [math], Kähler structures, Mathematics - Algebraic Geometry, symplectic manifold, Momentum maps; symplectic reduction, FOS: Mathematics, Algebraic Geometry (math.AG), meromorphic connections, Nonlinear Sciences - Exactly Solvable and Integrable Systems, monodromy map, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], [MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA], [MATH.MATH-SG] Mathematics [math]/Symplectic Geometry [math.SG], gauge theory, Differential Geometry (math.DG), symplectic structure, Mathematics - Symplectic Geometry, Symplectic structures of moduli spaces, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Symplectic Geometry (math.SG), isomonodromic deformations, Exactly Solvable and Integrable Systems (nlin.SI), [MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]
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