Stiefel-Whitney numbers of quaternionic and related manifolds

Floyd, E. E.

doi:10.1090/S0002-9947-1971-0273632-8

Stiefel-Whitney numbers of quaternionic and related manifolds
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Trans. Amer. Math. Soc. 155 (1971), 77-94 Request permission

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.

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The relation of cobordism to $K$-theories

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Novikov resolutions for symplectic cobordism