Cohomologías elípticas (Un ensayo introductorio)
- Autores: Guillermo Moreno
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 36, Nº 2, 2, 1992 (Ejemplar dedicado a: la memória de Pere Menal i Brufal), págs. 789-806
- Idioma: español
- DOI: 10.5565/publmat_362b92_05
- Títulos paralelos:
- Elliptic cohomologies: an introductory survey
- Enlaces
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Resumen
Let a and ß be any angles then the known formula sin (a+ß) = sina cosß + cosa sinß becomes under the substitution x = sina, y = sinß, sin (a + ß) = x v(1 - y2) + y v(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 vR(y) + y vR(x)/1 - ex2y2). For R(z) = 1 - 2dz2 + ez4 the above case corresponds to e=0, d=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.
