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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: https://doi.org/10.1090/S0065-9266-2011-00604-0
Published electronically: February 14, 2011
Keywords: Formal group,
equivariant cohomology
MSC: Primary 55N20, 55N22, 55N91, 14L05
Table of Contents
Chapters
- 1. Introduction
- 2. Multicurves
- 3. Differential forms
- 4. Equivariant projective spaces
- 5. Equivariant orientability
- 6. Simple examples
- 7. Formal groups from algebraic groups
- 8. Equivariant formal groups of product type
- 9. Equivariant formal groups over rational rings
- 10. Equivariant formal groups of pushout type
- 11. Equivariant Morava $E$-theory
- 12. A completion theorem
- 13. Equivariant formal group laws and complex cobordism
- 14. A counterexample
- 15. Divisors
- 16. Embeddings
- 17. Symmetric powers of multicurves
- 18. Classification of divisors
- 19. Local structure of the scheme of divisors
- 20. Generalised homology of Grassmannians
- 21. Thom isomorphisms and the projective bundle theorem
- 22. Duality
- 23. Further theory of infinite Grassmannians
- 24. Transfers and the Burnside ring
- 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.- M. Ando, M. J. Hopkins, and N. P. Strickland, Elliptic spectra, the Witten genus and the theorem of the cube, Invent. Math. 146 (2001), no. 3, 595–687. MR 1869850, DOI 10.1007/s002220100175
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