Symplectic Cobordism and the Computation of Stable Stems

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.