By Stanley O. Kochman

This ebook comprises autonomous but comparable papers. within the first, Kochman makes use of the classical Adams spectral series to check the symplectic cobordism ring $\Omega ^*_{Sp}$. Computing larger differentials, he exhibits that the Adams spectral series doesn't cave in. those computations are utilized to review the Hurewicz homomorphism, a dead ringer for $\Omega ^*_{Sp}$ within the unoriented cobordism ring, and clone of the sturdy homotopy teams of spheres in $\Omega ^*_{Sp}$. The constitution of $\Omega ^{-N}_{Sp}$ is set for $N\leq 100$. within the moment paper, Kochman makes use of the result of the 1st paper to research the symplectic Adams-Novikov spectral series converging to the solid homotopy teams of spheres. He makes use of a generalized lambda algebra to compute the $E_2$-term and to investigate this spectral series via measure 33.