Titlebook: Manifolds, Sheaves, and Cohomology; Torsten Wedhorn Textbook 2016 Springer Fachmedien Wiesbaden 2016 Bundles.Cohomology.Lie Groups.Manifol

使迷醉

Manifolds,ly .) for some . together with its sheaf of .-functions (. fixed) (respective of holomorphic functions). Hence we first define the abstract notion of a space together with a sheaf of .-algebras for some ring .. These are called .-ringed spaces. Then a real (respectively complex) premanifold will be

泥沼

Linearization of Manifolds,c analysis is approximating an open subspace . of . at a point by the linear space . itself by visualizing . as a tangent space to . at the given point. Another (less trivial) example is the derivative of a differentiable map . on . in a point that is the best approximation of . nearby this point by

开始从未

legislate

nephritis

Bundles, fiber bundles, where . is a projection. Moreover, one often endows twists with an additional datum that restricts the changes between different local isomorphisms of . and π to a fixed subsheaf of the sheaf all automorphisms of .. For fiber bundles this subsheaf will usually be given by a faithful

不给啤

Soft Sheaves,ifolds if ., for instance the structure sheaf. On the other hand the cohomology of soft sheaves vanishes, and this yields immediately several local-global principles. The chapter starts with the definition and general properties of soft sheaves. In particular we will see that every global section ha

RAFF

枕垫

Cohomology of Constant Sheaves,pace . singular cohomology with values in a ring . and the cohomology of the constant sheaf .. are equal. We deduce that .. is acyclic if . is contractible and locally contractible..Combining this result for . and the proper base change theorem we deduce homotopy invariance of cohomology of constant

ALIEN

EXPEL

Appendix B: The Language of Categories,mples. There will be almost no proofs in this chapter..We start by introducing categories and functors. Important concepts are the notion of an equivalence of categories and, more generally, the notion of adjoint functors. We then give a short reminder on several notions of ordered sets and prove th