| eBook ISBN: | 978-1-4704-0073-6 |
| Product Code: | MEMO/104/496.E |
| List Price: | $36.00 |
| MAA Member Price: | $32.40 |
| AMS Member Price: | $21.60 |
| eBook ISBN: | 978-1-4704-0073-6 |
| Product Code: | MEMO/104/496.E |
| List Price: | $36.00 |
| MAA Member Price: | $32.40 |
| AMS Member Price: | $21.60 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 104; 1993; 88 ppMSC: Primary 55; Secondary 57
This book contains two independent yet related papers. In the first, Kochman uses the classical Adams spectral sequence to study the symplectic cobordism ring \(\Omega ^*_{Sp}\). Computing higher differentials, he shows that the Adams spectral sequence does not collapse. These computations are applied to study the Hurewicz homomorphism, the image of \(\Omega ^*_{Sp}\) in the unoriented cobordism ring, and the image of the stable homotopy groups of spheres in \(\Omega ^*_{Sp}\). The structure of \(\Omega ^{-N}_{Sp}\) is determined for \(N\leq 100\). In the second paper, Kochman uses the results of the first paper to analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres. He uses a generalized lambda algebra to compute the \(E_2\)-term and to analyze this spectral sequence through degree 33.
ReadershipResearch mathematicians and graduate students specializing in algebraic topology.
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Table of Contents
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Chapters
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The symplectic cobordism ring III
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1. Introduction
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2. Higher differentials—Theory
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3. Higher differentials—Examples
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4. The Hurewicz homomorphism
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5. The spectrum msp
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6. The image of $\Omega ^*_{Sp}$ in $\mathfrak {N}^*$
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7. On the image of $\pi ^S_*$ in $\Omega ^*_{Sp}$
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8. The first hundred stems
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The symplectic Adams Novikov spectral sequence for spheres
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1. Introduction
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2. Structure of $M\,Sp_*$
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3. Construction of $\Lambda ^*_{Sp}$—The first reduction theorem
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4. Admissibility relations
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5. Construction of $\Lambda ^*_{Sp}$—The second reduction theorem
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6. Homology of $\Gamma ^*_{Sp}$—The Bockstein spectral sequence
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7. Homology of $\Lambda [\alpha _t]$ and $\Lambda [\eta \alpha _t]$
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8. The Adams-Novikov spectral sequence
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This book contains two independent yet related papers. In the first, Kochman uses the classical Adams spectral sequence to study the symplectic cobordism ring \(\Omega ^*_{Sp}\). Computing higher differentials, he shows that the Adams spectral sequence does not collapse. These computations are applied to study the Hurewicz homomorphism, the image of \(\Omega ^*_{Sp}\) in the unoriented cobordism ring, and the image of the stable homotopy groups of spheres in \(\Omega ^*_{Sp}\). The structure of \(\Omega ^{-N}_{Sp}\) is determined for \(N\leq 100\). In the second paper, Kochman uses the results of the first paper to analyze the symplectic Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres. He uses a generalized lambda algebra to compute the \(E_2\)-term and to analyze this spectral sequence through degree 33.
Research mathematicians and graduate students specializing in algebraic topology.
-
Chapters
-
The symplectic cobordism ring III
-
1. Introduction
-
2. Higher differentials—Theory
-
3. Higher differentials—Examples
-
4. The Hurewicz homomorphism
-
5. The spectrum msp
-
6. The image of $\Omega ^*_{Sp}$ in $\mathfrak {N}^*$
-
7. On the image of $\pi ^S_*$ in $\Omega ^*_{Sp}$
-
8. The first hundred stems
-
The symplectic Adams Novikov spectral sequence for spheres
-
1. Introduction
-
2. Structure of $M\,Sp_*$
-
3. Construction of $\Lambda ^*_{Sp}$—The first reduction theorem
-
4. Admissibility relations
-
5. Construction of $\Lambda ^*_{Sp}$—The second reduction theorem
-
6. Homology of $\Gamma ^*_{Sp}$—The Bockstein spectral sequence
-
7. Homology of $\Lambda [\alpha _t]$ and $\Lambda [\eta \alpha _t]$
-
8. The Adams-Novikov spectral sequence
