Introduction to stokes structures Claude Sabbah

Format:

Book

Author/Creator:

Sabbah, Claude

Series:

Lecture notes in mathematics (Springer-Verlag) 2060

Lecture notes in mathematics 1617-9692 2060

Language:

English

Subjects (All):

Differential equations, Linear.

Stokes' theorem.

Physical Description:

1 online resource

Place of Publication:

Berlin Springer ©2013

Language Note:

English

System Details:

text file

PDF

Summary:

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

Contents:

I-Filtrations Stokes-Filtered Local Systems in Dimension One Abelianity and Strictness Stokes-Perverse Sheaves on Riemann Surfaces The Riemann-Hilbert Correspondence for Holonomic -Modules on Curves Applications of the Riemann-Hilbert Correspondence to Holonomic Distributions Riemann-Hilbert and Laplace on the Affine Line (the Regular Case) Real Blow-Up Spaces and Moderate de Rham Complexes Stokes-Filtered Local Systems Along a Divisor with Normal Crossings The Riemann-Hilbert Correspondence for Good Meromorphic Connections (Case of a Smooth Divisor) Good Meromorphic Connections (Formal Theory) Good Meromorphic Connections (Analytic Theory) and the Riemann-Hilbert Correspondence Push-Forward of Stokes-Filtered Local Systems Irregular Nearby Cycles Nearby Cycles of Stokes-Filtered Local Systems

Notes:

Includes bibliographical references and index

Online resource; title from PDF title page (SpringerLink, viewed October 8, 2012)

Other Format:

Printed edition:

ISBN:

3642316956

9783642316951

OCLC:

812138227

Access Restriction:

Restricted for use by site license