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Symplectic Cobordism and the Computation of Stable Stems
Stanley O. Kochman
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Memoirs of the American Mathematical Society
1993; 88 pp; softcover
Volume: 104
ISBN-10: 0-8218-2558-5
ISBN-13: 978-0-8218-2558-7
List Price: US$34
Individual Members: US$20.40
Institutional Members: US$27.20
Order Code: MEMO/104/496
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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.

Readership

Research mathematicians and graduate students specializing in algebraic topology.

Table of Contents

  • The symplectic cobordism ring III
  • Introduction
  • Higher differentials-theory
  • Higher differentials-examples
  • The Hurewicz homomorphism
  • The spectrum msp
  • The image of \(\Omega ^\ast _{Sp}\) in \({\mathfrak N}^\ast\)
  • On the image of \(\pi ^S_\ast\) in \(\Omega ^\ast _{Sp}\)
  • The first hundred stems
  • The symplectic Adams Novikov spectral sequence for spheres
  • Introduction
  • Structure of \(MSp_\ast\)
  • Construction of \(\Lambda ^\ast _{Sp}\) -The first reduction theorem
  • Admissibility relations
  • Construction of \(\Lambda ^\ast _{Sp}\) -The second reduction theorem
  • Homology of \(\Gamma ^\ast _{Sp}\) -The Bockstein spectral sequence
  • Homology of \(\Lambda [\alpha _t]\) and \(\Lambda [\eta \alpha _t]\)
  • The Adams-Novikov spectral sequence
  • Bibliography
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