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# memo_has_moved_text();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: 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 $E$-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 $A$ be a finite abelian group. We set up an algebraic framework for studying $A$-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.