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 ofStokes 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 thecomplex 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 variousoperations on Stokes-filtered local systems are analyzed.
- ISBN: 978-3-642-31694-4
- Editorial: Springer
- Encuadernacion: Rústica
- Fecha Publicación: 30/09/2012
- Nº Volúmenes: 1
- Idioma: Inglés