Elliptic cohomologies: an introductory survey.

Moreno, Guillermo. "Elliptic cohomologies: an introductory survey.." Publicacions Matemàtiques 36.2B (1992): 789-806. <http://eudml.org/doc/41753>.

@article{Moreno1992,
abstract = {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.},
author = {Moreno, Guillermo},
journal = {Publicacions Matemàtiques},
keywords = {formal groups; elliptic functions; complex orientable cohomologies; elliptic cohomology},
language = {eng},
number = {2B},
pages = {789-806},
title = {Elliptic cohomologies: an introductory survey.},
url = {http://eudml.org/doc/41753},
volume = {36},
year = {1992},
}

TY - JOUR
AU - Moreno, Guillermo
TI - Elliptic cohomologies: an introductory survey.
JO - Publicacions Matemàtiques
PY - 1992
VL - 36
IS - 2B
SP - 789
EP - 806
AB - 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.
LA - eng
KW - formal groups; elliptic functions; complex orientable cohomologies; elliptic cohomology
UR - http://eudml.org/doc/41753
ER -