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 analyse 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 analyse this spectral sequence through degree 33.
Written for readers with a background in basic homotopy theory including computational methods in Adams spectral sequences, this book presents new methods for computing higher differentials in the classical Adams spectral sequence and shows how Adams spectral sequences can be used to compute homotopy groups of spectra. This book is directed towards mathematicians and graduate students specializing in algebraic topology.
Written for readers with a background in basic homotopy theory including computational methods in Adams spectral sequences, this book presents new methods for computing higher differentials in the classical Adams spectral sequence and shows how Adams spectral sequences can be used to compute homotopy groups of spectra. This book is directed towards mathematicians and graduate students specializing in algebraic topology.