Introduction to Stokes structures
- Claude Sabbah.
- Heidelberg ; New York : Springer, c2013.
- Physical description
- xiv, 249 p. : ill. ; 24 cm.
- Lecture notes in mathematics (Springer-Verlag) 2060.
Math & Statistics Library
QA3 .L28 V.2060
- Unknown QA3 .L28 V.2060
- Sabbah, Claude.
- Includes bibliographical references (p. 239-243) and indexes.
- 1. T-filtrations
- 2. Stokes-filtered local systems in dimension one
- 3. Abelianity and strictness
- 4. Stokes-perverse sheaves on Riemann surfaces
- 5. The Riemann-Hilbert correspondence for holonomic D-modules on curves
- 6. Applications of the Riemann-Hilbert correspondence to holonomic distributions
- 7. Riemann-Hilbert and Laplace on the affine line (the regular case)
- 8. Real blow-up spaces and moderate de Rham complexes
- 9. Stokes-filtered local systems along a divisor with normal crossings
- 10. The Riemann-Hilbert correspondence for good meromorphic connections (case of a smooth divisor)
- 11. Good meromorphic connections (formal theory)
- 12. Good meromorphic connections (analytic theory) and the Riemann-Hilbert correspondence
- 13. Push-forward of Stokes-filtered local systems
- 14. Irregular nearby cycles
- 15. Nearby cycles of Stokes-filtered 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 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.
(source: Nielsen Book Data)
- Publication date
- Lecture notes in mathematics, 0075-8434 ; 2060
- 9783642316944 (pbk.)
- 3642316948 (pbk.)