Description

Book Synopsis

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.



Table of Contents
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.

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

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A Hardback by Masaki Kashiwara, Pierre Schapira

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    View other formats and editions of Sheaves on Manifolds: With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel by Masaki Kashiwara

    Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
    Publication Date: 01/05/2002
    ISBN13: 9783540518617, 978-3540518617
    ISBN10: 3540518614

    Description

    Book Synopsis

    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.



    Table of Contents
    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.

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