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Proceedings of the American Mathematical Society
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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DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0270393-9
PII: S 0002-9939(1971)0270393-9
Keywords: Symplectic cobordism, stably symplectic manifolds, symplectic Pontrjagin numbers, characteristic numbers
Article copyright: © Copyright 1971 American Mathematical Society