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Symplectic Cobordism and the Computation of Stable Stems

Available Formats:
Electronic ISBN: 978-1-4704-0073-6
Product Code: MEMO/104/496.E
88 pp
List Price: $36.00 MAA Member Price:$32.40
AMS Member Price: $21.60 Click above image for expanded view Symplectic Cobordism and the Computation of Stable Stems Available Formats:  Electronic ISBN: 978-1-4704-0073-6 Product Code: MEMO/104/496.E 88 pp  List Price:$36.00 MAA Member Price: $32.40 AMS Member Price:$21.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 1041993
MSC: 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.

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
• 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
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Volume: 1041993
MSC: 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.

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
• 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 $\Lambda [\eta \alpha _t]$