Elliptic cohomologies: an introductory survey.

Título inglés Elliptic cohomologies: an introductory survey.
Título español Cohomologías elípticas: un ensayo introductorio.
Autor/es Moreno, Guillermo
Organización Dep. Mat. Cent. Inv. Estud. Avan. [CINVESTAV], México D.F., Méjico
Revista 0214-1493
Publicación 1992, 36 (2B): 789-806, 24 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés 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). For R(z) = 1 - 2δz2 + εz4 the above case corresponds to ε=0, δ=1/2.
In this survey paper we define these cohomology theories and establish their relationship with global analysis (Atiyah-Singer theorem) and modular forms following ideas of Landweber, Hirzebruch et al.
Código MathReviews MR1210020
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