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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$74
Individual Members: US$44.40
Institutional Members: US$59.20
Order Code: MEMO/213/1001
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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.

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
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