Author | Dimca, Alexandru. author |
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Title | Sheaves in Topology [electronic resource] / by Alexandru Dimca |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-3-642-18868-8 |
Descript | XVI, 240 p. online resource |
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 Poincarรฉ-Verdier Duality -- 3.1 Cohomological Dimension of Rings and Spaces -- 3.2 The Functor f! -- 3.3 Poincarรฉ 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