© 2013

Introduction to Stokes Structures


Part of the Lecture Notes in Mathematics book series (LNM, volume 2060)

Table of contents

About this book


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.


34M40, 32C38, 35A27 Meromorphic connection Stokes filtration Stokes-perverse sheaf real blowing-up

Authors and affiliations

  1. 1.Centre de mathématiquesCNRS Ecole polytechniquePalaiseauFrance

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