Nilpotence and Periodicity in Stable Homotopy Theory
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€107.99
A01=Douglas C. Ravenel
Abelian category
Abelian group
Adams spectral sequence
Affine space
Algebra homomorphism
Algebraic topology
Algebraic topology (object)
Atiyah-Hirzebruch spectral sequence
Author_Douglas C. Ravenel
Automorphism
Boolean algebra (structure)
Category of topological spaces
Category=PBPD
Classification theorem
Classifying space
Cohomology
Cohomology operation
Commutative algebra
Commutative ring
Complex projective space
Conjecture
Continuous function
Contractible space
Coproduct
CW complex
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Explicit formulae (L-function)
Functor
Groupoid
Homology (mathematics)
Homomorphism
Homotopy
Homotopy category
Homotopy group
Hopf algebra
Hurewicz theorem
Infinite product
Inverse limit
Irreducible representation
Isomorphism class
K-theory
Loop space
Mapping cone (homological algebra)
Mathematical induction
Modular representation theory
Module (mathematics)
Morava K-theory
Morphism
N-sphere
Noetherian
Noetherian ring
Noncommutative ring
P-adic number
Polynomial
Polynomial ring
Power series
Principal ideal domain
Ring (mathematics)
Ring homomorphism
Ring spectrum
Simplicial complex
Smash product
Special case
Spectral sequence
Steenrod algebra
Subcategory
Subquotient
Symmetric group
Tensor product
Theorem
Topological space
Topology
Zariski topology
Product details
- ISBN 9780691025728
- Weight: 312g
- Dimensions: 152 x 229mm
- Publication Date: 08 Nov 1992
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Douglas C. Ravenel is Professor of Mathematics at the University of Rochester.
