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.
Klappentext
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.
Inhalt
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.