Introduction to Stokes Structures

von Claude Sabbah

249 Seiten, Taschenbuch

Kurzbeschreibung des Verlags

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.

• Reihe: Lecture Notes in Mathematics
• ISBN: 9783642316944
• Sprache: Englisch
• Erscheinungsdatum: 04.10.2012
• Genre: Mathematik/Arithmetik, Algebra
• Verlag: Springer Berlin