On the image of symplectic cobordism in unoriented cobordism

Roush, Fred W.

doi:10.1090/S0002-9939-1973-0326764-7

On the image of symplectic cobordism in unoriented cobordism
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by Fred W. Roush

Proc. Amer. Math. Soc. 38 (1973), 647-652

DOI: https://doi.org/10.1090/S0002-9939-1973-0326764-7

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Abstract:

It is shown in this paper that all 16th powers of unoriented cobordism classes can be represented by stably almost symplectic manifolds. The generators are coefficients in the expansion of a Conner-Floyd characteristic class of the symplectification of a tensor product of symplectic line bundles.

References

P. E. Conner and E. E. Floyd, The relation of cobordism to $K$-theories, Lecture Notes in Mathematics, No. 28, Springer-Verlag, Berlin-New York, 1966. MR 0216511
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
Peter S. Landweber, On the symplectic bordism groups of the spaces $\textrm {Sp}(n)$, $\textrm {HP}(n)$, and $\textrm {BSp}(n)$, Michigan Math. J. 15 (1968), 145–153. MR 226649
Nigel Ray, A note on the symplectic bordism ring, Bull. London Math. Soc. 3 (1971), 159–162. MR 300295, DOI 10.1112/blms/3.2.159
D. M. Segal, On the symplectic cobordism ring, Comment. Math. Helv. 45 (1970), 159–169. MR 263094, DOI 10.1007/BF02567323
R. E. Stong, Some remarks on symplectic cobordism, Ann. of Math. (2) 86 (1967), 425–433. MR 219079, DOI 10.2307/1970608
Robert E. Stong, Notes on cobordism theory, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1968. Mathematical notes. MR 0248858