In mathematics, specifically in algebraic topology, the cup product is a method of adjoining two cocycles of degree p {\displaystyle p} and q {\displaystyle...

calculus Tensor product Product topology Cap product Cup product Slant product Smash product Wedge sum (or wedge product) Internal product, in a monoidal...

owned by Diageo since 1997. Its most popular product is Pimm's No. 1 Cup, commonly used for the Pimm's cup cocktail. Pimm's is dark brown with a reddish...

of the product are packaged in foam, plastic, or paper cups and prepared simply by adding boiling water. The product name actually began as Cup O' Noodles...

in 1923 by H. B. Reese in Hershey, Pennsylvania. The official product name was "Penny Cups" because they could be purchased for one cent. Reese had originally...

{\mathcal {P}}({\mathcal {P}}(A\cup B))} where P {\displaystyle {\mathcal {P}}} denotes the power set. Then the Cartesian product of the sets A {\displaystyle...

well. While the cup product of ordinary cohomology describes how submanifolds of the manifold intersect each other, the quantum cup product of quantum cohomology...

{\displaystyle X} . The most important cohomology theories have a product, the cup product, which gives them a ring structure. Because of this feature, cohomology...

curve C, then their wedge product is necessarily zero because C has only one complex dimension; consequently, the cup product of their cohomology classes...

X is a ring formed from the cohomology groups of X together with the cup product serving as the ring multiplication. Here 'cohomology' is usually understood...

with the interpretation of the cup product in terms of the Künneth formula, we can explain the existence of the cap product in the following way. Using CW...

\beta } where ∧ {\displaystyle \wedge } is the wedge product. The definition using cup product has a simpler analogue modulo 2 {\displaystyle 2} (which...

The cup product of two cocycles is again a cocycle, and the product of a coboundary with a cocycle (in either order) is a coboundary. The cup product operation...

In mathematics, specifically group theory, the free product is an operation that takes two groups G and H and constructs a new group G ∗ H. The result...

the Massey product is a cohomology operation of higher order introduced in (Massey 1958), which generalizes the cup product. The Massey product was created...

algebra: the algebraic structure arising on the cochain level for the cup product Poincaré duality: swaps some of these Intersection theory: for a similar...

theorem. Given a connected and oriented manifold M of dimension 4k, the cup product gives rise to a quadratic form Q on the 'middle' real cohomology group...

take cohomology with coefficients in a ring R {\displaystyle R} , the cup product squaring operation yields a family of cohomology operations: H n ( X...

company Keurig Dr Pepper manufactures the machines. The main Keurig products are K-Cup pods, which are single-serve coffee containers; other beverage pods;...

L\rightarrow 0\in \operatorname {Ext} ^{m}(L,M),} we form the Yoneda (cup) product ξ ⌣ ρ : 0 → N → E 0 → ⋯ → E n − 1 → F 0 → ⋯ → F m − 1 → L → 0 ∈ Ext m...

Carolyn Witter, and two children. Thanks to Lefschetz and others, the cup product structure of cohomology was understood by the early 1940s. Steenrod was...

Frito-Lay Press Release Archive. ""Tapatío Ramen" Instant Ramen Noodle Cup Product Featuring Tapatío Hot Sauce, Begins Initial West Coast Release of...

A cup noodle is an instant ramen product in a disposable cup, first developed in 1971 and manufactured by the Japanese food company Nissin Foods. The product...

Look up cup, CUP, Cup, ćup, cúp, cups, or CUPS in Wiktionary, the free dictionary. A cup is an open-top container used to hold liquids for pouring or drinking...

product on homology classes of any dimension, which is Poincaré dual to the cup product on cohomology. Like the cup product, the intersection product...

company Media Markt marketed a cupcake maker dubbed "2 Girls 1 Cup-Cake Maker". The product's slogan was that it made cupcakes "So good that it's impossible...

In mathematics, an empty product, or nullary product or vacuous product, is the result of multiplying no factors. It is by convention equal to the multiplicative...

isomorphism in Serre duality comes from the cup product in sheaf cohomology. Namely, the composition of the cup product with a natural trace map on H n ( X ...

homology or cohomology class in an appropriate space, or as the deformed cup product of quantum cohomology. These invariants have been used to distinguish...

consistency and shape led to the Clark Cup product, with misshaped bars ground and mixed with peanut butter for use as cup filling. The Clark Bar was relaunched...