| Document Type
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BL
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| Record Number
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969131
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| Doc. No
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b723501
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| Main Entry
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Ravenel, Douglas C.
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| Title & Author
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Complex cobordism and stable homotopy groups of spheres.
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| Publication Statement
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Burlington :: Elsevier Science,, 2014.
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| Series Statement
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Pure and Applied Mathematics ;; v. 121
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| Page. NO
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1 online resource (435 pages).
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| ISBN
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0080874401
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: 9780080874401
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| Contents
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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 <U+0073>(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.
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1. The Classical Adams Spectral Sequence2. 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).
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1. The Method of Infinite Descent2. 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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4. Beginning Calculations with the Adams-Novikov Spectral SequenceChapter 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 <U+0056>(n); 3. The Cohomology of <U+0056>(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.
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| Abstract
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Complex cobordism and stable homotopy groups of spheres.
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| Subject
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Cobordism theory.
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Homotopy groups.
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Spectral sequences (Mathematics)
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Sphere.
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| Dewey Classification
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510
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| LC Classification
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QA612.78 -- R37 1986eb
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