Introduction to Stokes structures
 Responsibility
 Claude Sabbah.
 Language
 English.
 Imprint
 Heidelberg ; New York : Springer, c2013.
 Physical description
 xiv, 249 p. : ill. ; 24 cm.
 Series
 Lecture notes in mathematics (SpringerVerlag) 2060.
Access
Available online
 www.springerlink.com
 dx.doi.org SpringerLink
Math & Statistics Library

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QA3 .L28 V.2060

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QA3 .L28 V.2060
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Creators/Contributors
 Author/Creator
 Sabbah, Claude.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 239243) and indexes.
 Contents

 1. Tfiltrations
 2. Stokesfiltered local systems in dimension one
 3. Abelianity and strictness
 4. Stokesperverse sheaves on Riemann surfaces
 5. The RiemannHilbert correspondence for holonomic Dmodules on curves
 6. Applications of the RiemannHilbert correspondence to holonomic distributions
 7. RiemannHilbert and Laplace on the affine line (the regular case)
 8. Real blowup spaces and moderate de Rham complexes
 9. Stokesfiltered local systems along a divisor with normal crossings
 10. The RiemannHilbert correspondence for good meromorphic connections (case of a smooth divisor)
 11. Good meromorphic connections (formal theory)
 12. Good meromorphic connections (analytic theory) and the RiemannHilbert correspondence
 13. Pushforward of Stokesfiltered local systems
 14. Irregular nearby cycles
 15. Nearby cycles of Stokesfiltered local systems.
 Publisher's 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 Stokesperverse sheaf. This point of view is generalized to holonomic systems of linear differential equations in the complex domain, and a general RiemannHilbert 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 Stokesfiltered local systems are analyzed.
(source: Nielsen Book Data)
Subjects
Bibliographic information
 Publication date
 2013
 Series
 Lecture notes in mathematics, 00758434 ; 2060
 ISBN
 9783642316944 (pbk.)
 3642316948 (pbk.)
 3642316956
 9783642316951