Introduction to Stokes Structures

Front Cover
Springer, Oct 3, 2012 - Mathematics - 249 pages
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

1 IFiltrations
1
Part I Dimension One
22
Part II Dimension Two and More
114
References
239

Other editions - View all

Common terms and phrases