Topological Invariants of Stratified Spaces

Markus Banagl9783540385851, 3-540-38585-1

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.

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Table of contents :
file_01……Page 1
file_02……Page 11
file_03……Page 36
file_04……Page 67
file_05……Page 79
file_06……Page 107
file_07……Page 131
file_08……Page 149
file_09……Page 168
file_10……Page 224
file_11……Page 249
file_12……Page 256