| Preface I Sheaves and Presheaves 1 Definitions 2 Homomorphisms， subsheaves， and quotient sheaves 3 Direct and inverse images 4 Cohomomorphisms 5 Algebraic constructions 6 Supports 7 Classical cohomology theories Exercises II Sheaf Cohomology I Differential sheaves and resolutions 2 The canonical resolution and sheaf cohomology 3 Injective sheaves 4 Acyclic sheaves 5 Flabby sheaves 6 Connected sequences of functors 7 Axioms for cohomology and the cup product 8 Maps of spaces 9 φ-soft and φ-fine sheaves 10 Subspaces 11 The Vietoris mapping theorem and homotopy invariance 12 Relative cohomology 13 Mayer-Vietoris theorems 14 Continuity 15 The Kiinneth and universal coefficient theorems 16 Dimension 17 Local connectivity 18 Change of supports; local cohomology groups 19 The transfer homomorphism and the Smith sequences 20 Steenrods cyclic re... |
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