Multicurves and equivariant cohomology / N. P. Strickland.

Format:

Book

Author/Creator:

Strickland, Neil P., 1966- author.

Series:

Memoirs of the American Mathematical Society ; Volume 213, Number 1001.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 213, Number 1001

Language:

English

Subjects (All):

Formal groups.

Homology theory.

Geometry, Algebraic.

Physical Description:

1 online resource (117 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2011.

Language Note:

English

Summary:

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.

Contents:

""Contents""; ""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""

""Bibliography""""Index""

Notes:

"Volume 213, Number 1001 (second of 5 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0618-7