Ebook: Topology of Singular Spaces and Constructible Sheaves

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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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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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.

Content:
Front Matter....Pages i-x
Introduction....Pages 1-16
Thom-Sebastiani Theorem for constructible sheaves....Pages 17-80
Constructible sheaves in geometric categories....Pages 81-140
Localization results for equivariant constructible sheaves....Pages 141-205
Stratification theory and constructible sheaves....Pages 207-268
Morse theory for constructible sheaves....Pages 269-373
Vanishing theorems for constructible sheaves....Pages 375-431
Back Matter....Pages 433-454

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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.

Content:
Front Matter....Pages i-x
Introduction....Pages 1-16
Thom-Sebastiani Theorem for constructible sheaves....Pages 17-80
Constructible sheaves in geometric categories....Pages 81-140
Localization results for equivariant constructible sheaves....Pages 141-205
Stratification theory and constructible sheaves....Pages 207-268
Morse theory for constructible sheaves....Pages 269-373
Vanishing theorems for constructible sheaves....Pages 375-431
Back Matter....Pages 433-454
....