Stiefel-Whitney numbers of quaternionic and related manifolds

Abstract

There is considered the image of the symplectic cobordism ring $\Omega _\ast ^{SP}$ in the unoriented cobordism ring ${N_\ast }$. A polynomial subalgebra of ${N_\ast }$ is exhibited, with all generators in dimensions divisible by 16, such that the image is contained in the polynomial subalgebra. The methods combine the $K$-theory characteristic numbers as used by Stong with the use of the Landweber-Novikov ring.