Electronic ISBN:  9781470400736 
Product Code:  MEMO/104/496.E 
List Price:  $36.00 
MAA Member Price:  $32.40 
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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 AdamsNovikov 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.

Table of Contents

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 AdamsNovikov 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 AdamsNovikov 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 AdamsNovikov spectral sequence