Sheaves in Topology (Hardcover)

1 Derived Categories.- 1.1 Categories of Complexes C (A).- 1.2 Homotopical Categories K (A).- 1.3 The Derived Categories D (A).- 1.4 The Derived Functors of Hom.- 2 Derived Categories in Topology.- 2.1 Generahties on Sheaves.- 2.2 Derived Tensor Products.- 2.3 Direct and Inverse Images.- 2.4 The Adjunction Triangle.- 2.5 Local Systems.- 3 Poincare-Verdier Duality.- 3.1 Cohomological Dimension of Rings and Spaces.- 3.2 The Functor f!.- 3.3 Poincare and Alexander Duality.- 3.4 Vanishing Results.- 4 Constructible Sheaves, Vanishing Cycles and Characteristic Varieties.- 4.1 Constructible Sheaves.- 4.2 Nearby and Vanishing Cycles.- 4.3 Characteristic Varieties and Characteristic Cycles.- 5 Perverse Sheaves.- 5.1 t-Structures and the Definition of Perverse.- 5.2 Properties of Perverse.- 5.3 D-Modules and Perverse.- 5.4 Intersection Cohomology.- 6 Applications to the Geometry of Singular Spaces.- Singularities, Milnor Fibers and Monodromy.- Topology of Deformations.- Topology of Polynomial Functions.- Hyperplane and Hypersurface Arrangements.- References.