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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Divisibility conditions on characteristic numbers of stably symplectic manifolds

Author: D. M. Segal
Journal: Proc. Amer. Math. Soc. 27 (1971), 411-415
MSC: Primary 57.32
MathSciNet review: 0270393
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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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Keywords: Symplectic cobordism, stably symplectic manifolds, symplectic Pontrjagin numbers, characteristic numbers
Article copyright: © Copyright 1971 American Mathematical Society

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