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Multicurves and Equivariant Cohomology
| eBook ISBN: | 978-1-4704-0618-9 |
| Product Code: | MEMO/213/1001.E |
| List Price: | $74.00 |
| MAA Member Price: | $66.60 |
| AMS Member Price: | $44.40 |
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Multicurves and Equivariant Cohomology
| eBook ISBN: | 978-1-4704-0618-9 |
| Product Code: | MEMO/213/1001.E |
| List Price: | $74.00 |
| MAA Member Price: | $66.60 |
| AMS Member Price: | $44.40 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 213; 2011; 117 ppMSC: Primary 55; 14;
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.
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Table of Contents
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Chapters
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1. Introduction
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2. Multicurves
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3. Differential forms
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4. Equivariant projective spaces
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5. Equivariant orientability
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6. Simple examples
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7. Formal groups from algebraic groups
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8. Equivariant formal groups of product type
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9. Equivariant formal groups over rational rings
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10. Equivariant formal groups of pushout type
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11. Equivariant Morava $E$-theory
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12. A completion theorem
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13. Equivariant formal group laws and complex cobordism
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14. A counterexample
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15. Divisors
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16. Embeddings
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17. Symmetric powers of multicurves
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18. Classification of divisors
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19. Local structure of the scheme of divisors
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20. Generalised homology of Grassmannians
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21. Thom isomorphisms and the projective bundle theorem
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22. Duality
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23. Further theory of infinite Grassmannians
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24. Transfers and the Burnside ring
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25. Generalisations
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RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
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Volume: 213; 2011; 117 pp
MSC: Primary 55; 14;
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.
-
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
Review Copy – for publishers of book reviews
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