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Multicurves and equivariant cohomology


About this Title

N. P. Strickland, Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH, United Kingdom

Publication: Memoirs of the American Mathematical Society
Publication Year 2011: Volume 213, Number 1001
ISBNs: 978-0-8218-4901-9 (print); 978-1-4704-0618-9 (online)
DOI: http://dx.doi.org/10.1090/S0065-9266-2011-00604-0
Published electronically: February 14, 2011
MathSciNet review: 2856125
Keywords: Formal group, equivariant cohomology
MSC (2010): Primary 55N20, 55N22, 55N91, 14L05

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Multicurves
  • Chapter 3. Differential forms
  • Chapter 4. Equivariant projective spaces
  • Chapter 5. Equivariant orientability
  • Chapter 6. Simple examples
  • Chapter 7. Formal groups from algebraic groups
  • Chapter 8. Equivariant formal groups of product type
  • Chapter 9. Equivariant formal groups over rational rings
  • Chapter 10. Equivariant formal groups of pushout type
  • Chapter 11. Equivariant Morava -theory
  • Chapter 12. A completion theorem
  • Chapter 13. Equivariant formal group laws and complex cobordism
  • Chapter 14. A counterexample
  • Chapter 15. Divisors
  • Chapter 16. Embeddings
  • Chapter 17. Symmetric powers of multicurves
  • Chapter 18. Classification of divisors
  • Chapter 19. Local structure of the scheme of divisors
  • Chapter 20. Generalised homology of Grassmannians
  • Chapter 21. Thom isomorphisms and the projective bundle theorem
  • Chapter 22. Duality
  • Chapter 23. Further theory of infinite Grassmannians
  • Chapter 24. Transfers and the Burnside ring
  • Chapter 25. Generalisations

Abstract


Let be a finite abelian group. We set up an algebraic framework for studying -equivariant complex-orientable cohomology theories in terms of a suitable kind of equivariant formal group. We compute the equivariant cohomology of many spaces in these terms, including projective bundles (and associated Gysin maps), Thom spaces, and infinite Grassmannians.

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