Sheaves on Manifolds: With a Short History. «Les Débuts de la Théorie Des Faisceaux». by Christian Houzel

ISBN-13: 9783642080821 / Angielski / Miękka / 2010 / 512 str.

Masaki Kashiwara; Pierre Schapira

Opis

From the reviews: This book is devoted to the study of sheaves by microlocal methods..(it) may serve as a reference source as well as a textbook on this new subject. Houzel's historical overview of the development of sheaf theory will identify important landmarks for students and will be a pleasure to read for specialists. Math. Reviews 92a (1992). The book is clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics.(...)The book can be strongly recommended to a younger mathematician enthusiastic to assimilate a new range of techniques allowing flexible application to a wide variety of problems. Bull. L.M.S. (1992)

Spis treści

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.

O autorze

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.