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Elliptic cohomologies: an introductory survey.

Guillermo Moreno (1992)

Publicacions Matemàtiques

Let α and β be any angles then the known formula sin (α+β) = sinα cosβ + cosα sinβ becomes under the substitution x = sinα, y = sinβ, sin (α + β) = x √(1 - y2) + y √(1 - x2) =: F(x,y). This addition formula is an example of "Formal group law", which show up in many contexts in Modern Mathematics.In algebraic topology suitable cohomology theories induce a Formal group Law, the elliptic cohomologies are the ones who realize the Euler addition formula (1778): F(x,y) =: (x √R(y) + y √R(x)/1 - εx2y2)....

Equivariant algebraic topology

Sören Illman (1973)

Annales de l'institut Fourier

Let G be a topological group. We give the existence of an equivariant homology and cohomology theory, defined on the category of all G -pairs and G -maps, which both satisfy all seven equivariant Eilenberg-Steenrod axioms and have a given covariant and contravariant, respectively, coefficient system as coefficients.In the case that G is a compact Lie group we also define equivariant C W -complexes and mention some of their basic properties.The paper is a short abstract and contains no proofs.

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