De Rham cohomology information

In mathematics, de Rham cohomology (named after Georges de Rham) is a tool belonging both to algebraic topology and to differential topology, capable...

study algebraic geometry, and it built on the work of Georges de Rham on de Rham cohomology. It has major applications in two settings: Riemannian manifolds...

characteristic p is the de Rham cohomology of a smooth lift of X to characteristic 0, while de Rham cohomology of X is the crystalline cohomology reduced mod p (after...

Schwartz's recent work on distributions. De Rham's work on these topics is now usually formulated in the language of cohomology theory, although he did not do so...

smooth manifold X, de Rham's theorem says that the singular cohomology of X with real coefficients is isomorphic to the de Rham cohomology of X, defined using...

compact support, and d be the standard exterior derivative. Then the de Rham cohomology groups with compact support H c q ( X ) {\displaystyle H_{\mathrm...

equestrian DeRham Farm in Philipstown, New York De Rham, Iselin & Moore De Rham curve De Rham cohomology De Rham invariant De Rham–Weil theorem Hodge–de Rham spectral...

^{2}(M)}{\stackrel {d}{\to }}\ \Omega ^{3}(M)\to \cdots } The cohomology of this complex is called the de Rham cohomology of M. Locally constant functions are designated...

possible to calculate its cohomology from the Lie algebra. This can be done as follows. Its cohomology is the de Rham cohomology of the complex of differential...

and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds. Let M be a complex...

lemma (pronounced ddbar lemma) is a mathematical lemma about the de Rham cohomology class of a complex differential form. The ∂ ∂ ¯ {\displaystyle \partial...

{\displaystyle \ell } , crystalline cohomology. The proofs of the axioms for Betti cohomology and de Rham cohomology are comparatively easy and classical...

k + 1 cohomology class e called the Euler class of the bundle. Discussion of the sequence is clearest with de Rham cohomology. There cohomology classes...

Here 'cohomology' is usually understood as singular cohomology, but the ring structure is also present in other theories such as de Rham cohomology. It...

this kind on an arbitrary differentiable manifold are the subject of de Rham cohomology, which allows one to obtain purely topological information using differential...

as the differential (coboundary) to define de Rham cohomology on a manifold. The k-th de Rham cohomology (group) is the vector space of closed k-forms...

k-chains. Stokes' theorem says that this is a chain map from de Rham cohomology to singular cohomology with real coefficients; the exterior derivative, d, behaves...

cohomology groups in the Hn(G, M) → Hn(G, N). Similarly to other cohomology theories in topology and geometry, such as singular cohomology or de Rham...

complex is called the de Rham complex, and its cohomology is by definition the de Rham cohomology of M. By the Poincaré lemma, the de Rham complex is locally...

}^{p}(\log X))\cong {\text{Prim}}^{p-1,q}(X)} . In turns out the de Rham cohomology group H d R n + 1 ( P n + 1 − X ) {\displaystyle H_{dR}^{n+1}(\mathbb...

visualized. More specifically, the conjecture states that certain de Rham cohomology classes are algebraic; that is, they are sums of Poincaré duals of...

cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds...