Topology of Singular Spaces and Constructible Sheaves
By: by Jörg Schürmann
Series: Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) -- 63; Monografie Matematyczne, Instytut Matematyczny Polskiej Akademii Nauk (IMPAN) -- 63
Publisher: Birkhäuser Basel; Imprint: Birkhäuser
Published: 2003
Place of publication: Basel
Language: eng
Format: [electronic resource] /
Number of pages: 454
ISBN-13: 9783034894241; 9783034880619
Subjects: Mathematics; Algebraic Geometry; Algebraic topology; Algebra
Description: Assuming that the reader is familiar with sheaf theory, the book gives a self-contained introduction to the theory of constructible sheaves related to many kinds of singular spaces, such as cell complexes, triangulated spaces, semialgebraic and subanalytic sets, complex algebraic or analytic sets, stratified spaces, and quotient spaces. The relation to the underlying geometrical ideas are worked out in detail, together with many applications to the topology of such spaces. All chapters have their own detailed introduction, containing the main results and definitions, illustrated in simple terms by a number of examples. The technical details of the proof are postponed to later sections, since these are not needed for the applications.
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Table of contents: title: Introduction; title: 1. Thom-Sebastiani Theorem for Constructible Sheaves; title: 2. Constructible Sheaves in Geometric Categories; title: 3. Localization Results for Equivariant Constructible Sheaves; title: 4. Stratification Theory and Constructible Sheaves; title: 5. Morse Theory for Constructible Sheaves; title: 6. Vanishing Theorems for Constructible Sheaves; title: Bibliography; title: Index.