Some applications of Landweber-Novikov operations

Segal, David M.

doi:10.1090/S0002-9939-1976-0388419-5

Some applications of Landweber-Novikov operations
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by David M. Segal

Proc. Amer. Math. Soc. 54 (1976), 342-344

DOI: https://doi.org/10.1090/S0002-9939-1976-0388419-5

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Abstract:

Previous results on the characteristic numbers of $Sp$-manifolds are extended in three different ways. I. It is shown that the primitive symplectic Pontrjagin class evaluated on a $4({2^j} - 1)$ dimensional $Sp$-manifold always gives a number divisible by $8$. This forms an analogue to a well-known result of Milnor concerning $U$-manifolds. II. It is shown that some of the results of Floyd as well as an analogue of the previous result can be obtained for ’pseudo-symplectic’ manifolds. III. Results are generalised to $(Sp,fr)$ manifolds.

References

S. P. Novikov’s work on operations on complex cobordism

E. E. Floyd, Stiefel-Whitney numbers of quaternionic and related manifolds, Trans. Amer. Math. Soc. 155 (1971), 77–94. MR 273632, DOI 10.1090/S0002-9947-1971-0273632-8
D. M. Segal, Divisibility conditions on characteristic numbers of stably symplectic manifolds, Proc. Amer. Math. Soc. 27 (1971), 411–415. MR 270393, DOI 10.1090/S0002-9939-1971-0270393-9
R. E. Stong, Some remarks on symplectic cobordism, Ann. of Math. (2) 86 (1967), 425–433. MR 219079, DOI 10.2307/1970608

Bibliographic Information

Journal: Proc. Amer. Math. Soc. 54 (1976), 342-344
DOI: https://doi.org/10.1090/S0002-9939-1976-0388419-5
MathSciNet review: 0388419