Topological Invariants of Stratified Spaces

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.

After carefully introducing sheaf theory, derived categories,
Verdier duality, stratification theories, intersection homology,
t-structures and perverse sheaves, the ultimate objective is to explain
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.