Topological Invariants of Stratified Spaces
By: Banagl, M [author.].
Contributor(s): SpringerLink (Online service)0.
Material type:
BookSeries: Springer Monographs in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.Description: XII, 264 p. 14 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540385875.Subject(s): Mathematics | Differential geometry | Topology | Algebraic topology.1 | Mathematics.2 | Topology.2 | Differential Geometry.2 | Algebraic Topology.2DDC classification: 514 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode | Item holds |
|---|---|---|---|---|---|---|
| PK Kelkar Library, IIT Kanpur | Available | EBK9316 |
Elementary Sheaf Theory -- Homological Algebra -- Verdier Duality -- Intersection Homology -- Characteristic Classes and Smooth Manifolds -- Invariants of Witt Spaces -- T-Structures -- Methods of Computation -- Invariants of Non-Witt Spaces -- L2 Cohomology.
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. 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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