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Topological Invariants of Stratified Spaces
Hardcover
Series: Springer Monographs in Mathematics
ISBN13: 9783540385851
Publisher: Springer Nature
Published: Jan 9 2007
Pages: 264
Weight: 1.20
Height: 0.82 Width: 6.37 Depth: 9.38
Language: English
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.
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.
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