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EQUIVARIANT FORMAL GROUP LAWS

Published online by Cambridge University Press:  19 October 2000

MICHAEL COLE ,
J. P. C. GREENLEES  and
I. KRIZ
MICHAEL COLE
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA, mmcole@math.lsa.umich.edu
J. P. C. GREENLEES
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Hicks Building, Sheffield S3 7RH, j.greenlees@sheffield.ac.uk
I. KRIZ
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1109, USA, ikriz@math.lsa.umich.edu
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Abstract

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 orientedcohomology 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 thatthere 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. Westudy a number of topological cases in some detail. 1991 Mathematics Subject Classification: 14L05, 55N22, 55N91, 57R85.

Keywords

formal group lawcomplex orientationequivariant cohomologyequivariant cobordismLazard ringEuler class
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 81 , Issue 2 , September 2000 , pp. 355 - 386
Copyright
© 1999 London Mathematical Society

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