Complex Cobordism and Stable Homotopy Groups of Spheres

Name: Complex Cobordism and Stable Homotopy Groups of Spheres
Brand: Academic Press
Price: 54.95 EUR
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Unknown Author(Herausgeber*in)

Academic Press

Erschienen am 5. Mai 1986

412 Seiten

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Front Cover
COMPLEX COBORDISM AND STABLE HOMOTOPY GROUPS OF SPHERES
Copyright Page
Contents
Preface
Notations and Commonly Used Abbreviations
Chapter 1. An Introduction to the Homotopy Groups of Spheres
1. Classical Theorems Old and New
2. Methods of Computing p(Sn)
3. The Adams-Novikov E2-Term, Formal Group Laws, and the Greek Letter Construction
4. More Formal Group Law Theory, BP-Theory, Morava's Point of View, and the Chromatic Spectral Sequence
5. Unstable Homotopy Groups and the EHP Spectral Sequence
Chapter 2. Setting Up the Adams Spectral Sequence
1. The Classical Adams Spectral Sequence
2. The Adams Spectral Sequence Based on a Generalized Homology Theory
3. The Smash Product Pairing and the Generalized Connecting Homomorphism
Chapter 3. The Classical Adams Spectral Sequence
1. The Steenrod Algebra and Some Easy Calculations
2. The May Spectral Sequence
3. The Lambda Algebra
4. Some General Properties of Ext
5. Survey and Further Reading
Chapter 4. BP-Theory and the Adams-Novikov Spectral Sequence
1. Quillen's Theorem and the Structure of BP*(BP)
2. A Survey of BP-Theory
3. Some Calculations in BP*(BP)
4. Beginning Calculations with the Adams-Novikov Spectral Sequence
Chapter 5. The Chromatic Spectral Sequence
1. The Algebraic Construction
2. Ext1(BP*/In) and Hopf Invariant One
3. Ext(M1) and the J-Homomorphism
4. Ext2 and the Thom Reduction
5. Periodic Families in Ext2
6. Elements in Ext3 and Beyond
Chapter 6. Morava Stabilizer Algebras
1. The Change-of-Rings Isomorphism
2. The Structure of S(n)
3. The Cohomology of S(n)
4. The Odd Primary Kervaire Invariant Elements
5. The Spectra T(n)
Chapter 7. Computing Stable Homotopy Groups with the Adams - Novikov Spectral Sequence
1. The Method of Infinite Descent
2. The Complex C1,1
3. The Homotopy Groups of a Complex with p Cells
4. The ''Algorithm'' and Computations at p = 3
5. Computations for p = 5
Appendix 1. Hopf Algebras and Hopf Algebroids
1. Basic Definitions
2. Homological Algebra
3. Some Spectral Sequences
4. Massey Products
5. Algebraic Steenrod Operations
Appendix 2. Formal Group Laws
1. Universal Formal Group Laws and Strict Isomorphisms
2. Classification and Endomorphism Rings
Appendix 3. Tables of Homotopy Groups of Spheres
References
Index

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