# Elliptic cohomologies: an introductory survey.

Publicacions Matemàtiques (1992)

- Volume: 36, Issue: 2B, page 789-806
- ISSN: 0214-1493

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topMoreno, 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 -

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