Introduction to Stokes Structures |
|
Author:
| Sabbah, Claude |
Series title: | Lecture Notes in Mathematics Ser. |
ISBN: | 978-3-642-31694-4 |
Publication Date: | Oct 2012 |
Publisher: | Springer Berlin / Heidelberg
|
Imprint: | Springer |
Book Format: | Paperback |
List Price: | USD $59.99 |
Book Description:
|
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...
More DescriptionThis 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.