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Equivariant Formal Group Laws
Author(s) -
Cole Michael,
Greenlees J. P. C.,
Kriz I.
Publication year - 2000
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s0024611500012466
Subject(s) - formal group , mathematics , equivariant cohomology , equivariant map , cohomology , pure mathematics , abelian group , group (periodic table) , group cohomology , classifying space , lie group , flag (linear algebra) , algebra over a field , coproduct , ring (chemistry) , chemistry , organic chemistry
Motivated by complex oriented equivariant cohomology theories, we give a natural algebraic definition of an A ‐equivariant formal group law for any abelian compact Lie group A . The complex oriented cohomology of the classifying space for line bundles gives an example. We also show how the choice of a complete flag gives rise to a basis and a means of calculation. This allows us to deduce that there is a universal ring L A for A ‐equivariant formal group laws and that it is generated by the Euler classes and the coefficients of the coproduct of the orientation. We study a number of topological cases in some detail. 1991 Mathematics Subject Classification : 14L05, 55N22, 55N91, 57R85.