Memoirs of the American Mathematical Society 2011; 117 pp; softcover Volume: 213 ISBN10: 0821849018 ISBN13: 9780821849019 List Price: US$74 Individual Members: US$44.40 Institutional Members: US$59.20 Order Code: MEMO/213/1001
 Let \(A\) be a finite abelian group. The author sets up an algebraic framework for studying \(A\)equivariant complexorientable cohomology theories in terms of a suitable kind of equivariant formal group. He computes the equivariant cohomology of many spaces in these terms, including projective bundles (and associated Gysin maps), Thom spaces, and infinite Grassmannians. Table of Contents  Introduction
 Multicurves
 Differential forms
 Equivariant projective spaces
 Equivariant orientability
 Simple examples
 Formal groups from algebraic groups
 Equivariant formal groups of product type
 Equivariant formal groups over rational rings
 Equivariant formal groups of pushout type
 Equivariant Morava \(E\)theory
 A completion theorem
 Equivariant formal group laws and complex cobordism
 A counterexample
 Divisors
 Embeddings
 Symmetric powers of multicurves
 Classification of divisors
 Local structure of the scheme of divisors
 Generalised homology of Grassmannians
 Thom isomorphisms and the projective bundle theorem
 Duality
 Further theory of infinite Grassmannians
 Transfers and the Burnside ring
 Generalisations
 Bibliography
 Index
