Search results

continuous map f: X → Y of topological spaces and a ring R, the pullback along f on cohomology theory is a grade-preserving R-algebra homomorphism: f ∗ : H...

Pullback (cohomology) The pullback bundle is an example that bridges the notion of a pullback as precomposition, and the notion of a pullback as a Cartesian...

homology and a pullback homomorphism f ∗ : H i ( Y ) → H i ( X ) {\displaystyle f^{*}:H^{i}(Y)\to H^{i}(X)} on cohomology. This makes cohomology into a contravariant...

with another version of cohomology such as singular cohomology. For a continuous map f: X → Y and an abelian group A, the pullback sheaf f*(AY) is isomorphic...

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

In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients...

In mathematics, cohomology with compact support refers to certain cohomology theories, usually with some condition requiring that cocycles should have...

In algebraic topology, a complex-orientable cohomology theory is a multiplicative cohomology theory E such that the restriction map E 2 ( C P ∞ ) → E 2...

back or pullback may refer to: Pullback, a name given to two different mathematical processes Pullback (cohomology), a term in topology Pullback (differential...

map π {\displaystyle \pi } induces a map in cohomology H ∗ {\displaystyle H^{\ast }} called its pullback π ∗ {\displaystyle \pi ^{\ast }} π ∗ : H ∗ (...

the flatness assumption, provided that the pullback X ′ {\displaystyle X'} is replaced by the homotopy pullback. In the easiest case when X, S, and S ′ {\displaystyle...

existence of pullback maps in other situations, such as pullback homomorphisms in de Rham cohomology. Formally, let f : M → N be smooth, and let ω be a smooth...

whose pullbacks are the same bundle V, the maps must be homotopic. Therefore, the pullback by either f or g of any universal Chern class to a cohomology class...

dual of pullback Direct image sheaf, the pushforward of a sheaf by a map Fiberwise integral, the direct image of a differential form or cohomology by a smooth...

left is the class of the pullback of P to Y; on the right is the image of the class of P under the induced map in cohomology. Characteristic classes are...

for a very general cohomology theory, which encompasses also the "usual" topological cohomology theories such as singular cohomology. Especially in algebraic...

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

been used to define other cohomology theories since then, such as ℓ-adic cohomology, flat cohomology, and crystalline cohomology. While Grothendieck topologies...

isomorphic to the pullback of the universal bundle. This classifying map can be used to define the Stiefel-Whitney class of L, in the first cohomology of X with...

A homotopy pullback (or homotopy fiber-product) is the dual concept of a homotopy pushout.It satisfies the universal property of a pullback up to homotopy...