Topological Invariants of Stratified Spaces

The central theme of this book is the restoration of Poincar? duality on stratified singular spaces by using Verdier-self-dual sheaves such as the prototypical intersection chain sheaf on a complex variety.

The book first carefully introduces sheaf theory, derived categories, Verdier duality, stratification theories, intersection homology, t-structures and perverse sheaves. It then explains the construction as well as algebraic and geometric properties of invariants such as the signature and characteristic classes effectuated by self-dual sheaves.

Highlights never before presented in book form include complete and very 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.