Introduction to Stokes Structures

Introduction to Stokes Structures

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This research monograph provides a geometric description of holonomic differential systems in one or more variables. Stokes matrices form the extended monodromy data for a linear differential equation of one complex variable near an irregular singular point. The present volume presents the approach in terms of Stokes filtrations. For linear differential equations on a Riemann surface, it also develops the related notion of a Stokes-perverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general Riemann-Hilbert correspondence is proved for vector bundles with meromorphic connections on a complex manifold. Applications to the distributions solutions to such systems are also discussed, and various operations on Stokes-filtered local systems are analyzed.The map 2 : 0Yile a€“ s: is the composed map S: X Sa#39; x [0, co) a€“ S X S a†’ S. (o, B) H 0.6, so, in this chart, aamp; aquot;(6) s: Saquot; A— [0, co) ... 2) mod 27t. Conclusion. The complex DRaquot; (aamp;aquot;)0, on 2aquot; (6) has cohomology in degree 0 only, and is the constant sheafanbsp;...

Title:Introduction to Stokes Structures
Author:Claude Sabbah
Publisher:Springer - 2012-10-03


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