Topological Invariants of Stratified Spaces

The central theme of this book is the restoration of Poincaré dualityon stratified singular spaces by using Verdier-self-dual sheaves suchas the prototypical intersection chain sheaf on a complex variety.§After carefully introducing sheaf theory, derived categories, Verdier duality, stratification theories, intersection homology, t-structures and perverse sheaves, the ultimate objective is to explainthe construction as well as algebraic and geometric properties ofinvariants such as the signature and characteristic classes effectuatedby self-dual sheaves.§Highlights never before presented in book form include complete andvery detailed proofs of decomposition theorems for self-dual sheaves,explanation of methods for computing twisted characteristic classesand an introduction to the author's theory of non-Witt spaces andLagrangian structures.The central theme of this book is the restoration of Poincaré duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety. Highlights include complete and detailed proofs of decomposition theorems for self-dual sheaves, explanation of methods for computing twisted characteristic classes and an introduction to the author's theory of non-Witt spaces and Lagrangian structures.