Memoirs of the American Mathematical Society 1993; 88 pp; softcover Volume: 104 ISBN10: 0821825585 ISBN13: 9780821825587 List Price: US$36 Individual Members: US$21.60 Institutional Members: US$28.80 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 AdamsNovikov 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 differentialstheory
 Higher differentialsexamples
 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 AdamsNovikov spectral sequence
 Bibliography
