# Symplectic Cobordism and the Computation of Stable Stems

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*Stanley O. Kochman*

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.

#### Table of Contents

# Table of Contents

## Symplectic Cobordism and the Computation of Stable Stems

- CONTENTS v6 free
- THE SYMPLECTIC COBORDISM RING III 112 free
- THE SYMPLECTIC ADAMS NOVIKOV SPECTRAL SEQUENCE FOR SPHERES 4556
- 1 Introduction 4556
- 2 Structure of M S[sub(p)][sub(*)] 4859
- 3 Construction of ∧*[sub(sp)] - The First Reduction Theorem 5162
- 4 Admissibility Relations 5566
- 5 Construction of ∧*[sub(sp)] - The Second Reduction Theorem 6071
- 6 Homology of T*[sub(sp)] - The Bockstein Spectral Sequence 7182
- 7 Homology of ∧ [a[sub(t)]] and ∧ [ηα[sub(t)]] 7687
- 8 The Adams-Novikov Spectral Sequence 8192

- BIBLIOGRAPHY 8798