Divisibility conditions on characteristic numbers of stably symplectic manifolds

Segal, D. M.

doi:10.1090/S0002-9939-1971-0270393-9

Divisibility conditions on characteristic numbers of stably symplectic manifolds
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Proc. Amer. Math. Soc. 27 (1971), 411-415 Request permission

Abstract:

It is shown that every cohomology characteristic number of an $8k + 4$ [resp. $16k + 8$] dimensional stably symplectic manifold is divisible by 4 [resp. 2] and that certain characteristic numbers of $2$-dimensional stably symplectic manifolds are divisible by 2 and 4. The proofs depend on symplectic cobordism operations. Using explicit manifold constructions of Stong [5] it is shown that these results are to a large extent the best possible.

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