Author | Iversen, Birger. author |
---|---|
Title | Cohomology of Sheaves [electronic resource] / by Birger Iversen |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1986 |
Connect to | http://dx.doi.org/10.1007/978-3-642-82783-9 |
Descript | XII, 464 p. online resource |
I. Homological Algebra -- 1. Exact categories -- 2. Homology of complexes -- 3. Additive categories -- 4. Homotopy theory of complexes -- 5. Abelian categories -- 6. Injective resolutions -- 7. Right derived functors -- 8. Composition products -- 9. Resume of the projective case -- 10. Complexes of free abelian groups -- 11. Sign rules -- II. Sheaf Theory -- 0. Direct limits of abelian groups -- 1. Presheaves and sheaves -- 2. Localization -- 3. Cohomology of sheaves -- 4. Direct and inverse image of sheaves. f*,f* -- 5. Continuous maps and cohomology!, -- 6. Locally closed subspaces, h!h -- 7. Cup products -- 8. Tensor product of sheaves -- 9. Local cohomology -- 10. Cross products -- 11. Flat sheaves -- 12. Hom(E,F) -- III. Cohomology with Compact Support -- 1. Locally compact spaces -- 2. Soft sheaves -- 3. Soft sheaves on $$\mathbb {R}$$n -- 4. The exponential sequence -- 5. Cohomology of direct limits -- 6. Proper base change and proper homotopy -- 7. Locally closed subspaces -- 8. Cohomology of the n-sphere -- 9. Dimension of locally compact spaces -- 10. Wilderโs finiteness theorem -- IV. Cohomology and Analysis -- 1. Homotopy invariance of sheaf cohomology -- 2. Locally compact spaces, countable at infinity -- 3. Complex logarithms -- 4. Complex curve integrals. The monodromy theorem -- 5. The inhomogenous Cauchy-Riemann equations -- 6. Existence theorems for analytic functions -- 7. De Rham theorem -- 8. Relative cohomology -- 9. Classification of locally constant sheaves -- V. Duality with Coefficient in a Field -- 1. Sheaves of linear forms -- 2. Verdier duality -- 3. Orientation of topological manifolds -- 4. Submanifolds of $$\mathbb {R}$$n of codimension 1 -- 5. Duality for a subspace -- 6. Alexander duality -- 7. Residue theorem for n-1 forms on $$\mathbb {R}$$n -- VI. Poincare Duality with General Coefficients -- 1. Verdier duality -- 2. The dualizing complex D -- 3. Lefschetz duality -- 4. Algebraic duality -- 5. Universal coefficients -- 6. Alexander duality -- VII. Direct Image with Proper Support -- 1. The functor f! -- 2. The Kรผnneth formula -- 3. Global form of Verdier duality -- 4. Covering spaces -- 5. Local form of Verdier duality -- VIII. Characteristic Classes -- 1. Local duality -- 2. Thom class -- 3. Oriented microbundles -- 4. Cohomology of real projective space -- 5. Stiefel-Whitney classes -- 6. Chern classes -- 7. Pontrjagin classes -- IX. Borel Moore Homology -- 1. Proper homotopy invariance -- 2. Restriction maps -- 3. Cap products -- 4. Poincare duality -- 5. Cross products and the Kรผnneth formula -- 6. Diagonal class of an oriented manifold -- 7. Gysin maps -- 8. Lefschetz fixed point formula -- 9. Wuโs formula -- 10. Preservation of numbers -- 11. Trace maps in homology -- X. Application to Algebraic Geometry -- 1. Dimension of algebraic varieties -- 2. The cohomology class of a subvariety -- 3. Homology class of a subvariety -- 4. Intersection theory -- 5. Algebraic families of cycles -- 6. Algebraic cycles and Chern classes -- XI. Derived Categories -- 1. Categories of fractions -- 2. The derived category D (A) -- 3. Triangles associated to an exact sequence -- 4. Yoneda extensions -- 5. Octahedra -- 6. Localization