Introduction to Stokes Structures
Author | : Claude Sabbah |
Publisher | : Springer |
Total Pages | : 254 |
Release | : 2012-10-03 |
ISBN-10 | : 9783642316951 |
ISBN-13 | : 3642316956 |
Rating | : 4/5 (956 Downloads) |
Download or read book Introduction to Stokes Structures written by Claude Sabbah and published by Springer. This book was released on 2012-10-03 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.