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Multicurves and Equivariant Cohomology
N. P. Strickland, University of Sheffield, England
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Memoirs of the American Mathematical Society
2011; 117 pp; softcover
Volume: 213
ISBN-10: 0-8218-4901-8
ISBN-13: 978-0-8218-4901-9
List Price: US$70 Individual Members: US$42
Institutional Members: US\$56
Order Code: MEMO/213/1001

Let $$A$$ be a finite abelian group. The author sets up an algebraic framework for studying $$A$$-equivariant complex-orientable 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.

• 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