Lecture Notes in Mathematics

Sabbah, Claude

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.

Details

Published by: Springer

Publication Date: 2012-10-04

Format: Paperback

ISBN-13: 9783642316944

DOI: 10.1007/978-3-642-31695-1

Dimensions: 235cm x155cm

Pages: 249