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Symplectic Cobordism and the Computation of Stable Stems
 
Front Cover for 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
Front Cover for Symplectic Cobordism and the Computation of Stable Stems
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  • Front Cover for Symplectic Cobordism and the Computation of Stable Stems
  • Back Cover for Symplectic Cobordism and the Computation of Stable Stems
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.

    Readership

    Research 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 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.

Readership

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
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