Topology Of Singular Spaces And Constructible Sheaves (monografie Matematyczne)

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. This volume is based on the lecture notes of six courses delivered at a Cimpa Summer School in Temuco, Chile, in January 2001. Leading experts contribute with introductory articles covering a broad area in probability and its applications, such as mathematical physics and mathematics of finance. Written at graduate level, the lectures touch the latest advances on each subject, ranging from classical probability theory to modern developments. Thus the book will appeal to students, teachers and researchers working in probability theory or related fields. 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 Introduction 1. Thom-Sebastiani Theorem for Constructible Sheaves 2. Constructible Sheaves in Geometric Categories 3. Localization Results for Equivariant Constructible Sheaves 4. Stratification Theory and Constructible Sheaves 5. Morse Theory for Constructible Sheaves 6. Vanishing Theorems for Constructible Sheaves Bibliography Index.