Introduction to Stokes Structures

  • Claude Sabbah

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

Table of contents

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Claude Sabbah
    • 1
  1. 1.Centre de mathématiquesCNRS Ecole polytechniquePalaiseauFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-31695-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2013
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-31694-4
  • Online ISBN 978-3-642-31695-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book