Masaki Kashiwara, Pierre Schapira

Sheaves on Manifolds (eBook, PDF)

With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel

• Format: PDF

Produktbeschreibung

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view.

From the reviews:

"Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." -Bulletin of the L.M.S.

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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 512
• Erscheinungstermin: 14. März 2013
• Englisch
• ISBN-13: 9783662026618
• Artikelnr.: 53384530

Autorenporträt

Sheaf Theory is a highly "modern" and active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. In this Grundlehren volume the authors achieve a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view.

Inhaltsangabe

A Short History: Les débuts de la théorie des faisceaux.- I. Homological algebra.- II. Sheaves.- III. Poincaré-Verdier duality and Fourier-Sato transformation.- IV. Specialization and microlocalization.- V. Micro-support of sheaves.- VI. Micro-support and microlocalization.- VII. Contact transformations and pure sheaves.- VIII. Constructible sheaves.- IX. Characteristic cycles.- X. Perverse sheaves.- XI. Applications to O-modules and D-modules.- Appendix: Symplectic geometry.- Summary.- A.1. Symplectic vector spaces.- A.2. Homogeneous symplectic manifolds.- A.3. Inertia index.- Exercises to the Appendix.- Notes.- List of notations and conventions.