Lecture Notes in Mathematics

Introduction to Stokes Structures

Authors: Sabbah, Claude

  • A first part on the classical theory of linear differential equations in the complex domain revisited from a geometric view point. Original and new study of the Stokes phenomenon in higher dimension. Application to classical problems in distribution theory.

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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.

Table of contents (15 chapters)

  • $$\mathcal{I}$$ -Filtrations

    Sabbah, Claude

    Pages 1-19

  • Stokes-Filtered Local Systems in Dimension One

    Sabbah, Claude

    Pages 23-38

  • Abelianity and Strictness

    Sabbah, Claude

    Pages 39-50

  • Stokes-Perverse Sheaves on Riemann Surfaces

    Sabbah, Claude

    Pages 51-64

  • The Riemann–Hilbert Correspondence for Holonomic $$\mathcal{D}$$ -Modules on Curves

    Sabbah, Claude

    Pages 65-78

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-31695-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-31694-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Introduction to Stokes Structures
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2060
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-31695-1
DOI
10.1007/978-3-642-31695-1
Softcover ISBN
978-3-642-31694-4
Series ISSN
0075-8434
Edition Number
1
Number of Pages
XIV, 249
Number of Illustrations and Tables
13 b/w illustrations, 1 illustrations in colour
Topics