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Symplectic Cobordism and the Computation of Stable Stems
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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

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.

• 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
• 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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