Halving the Milnor manifolds and some conjectures of Ray

Segal, David M.

doi:10.1090/S0002-9939-1973-0368041-4

Halving the Milnor manifolds and some conjectures of Ray
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by David M. Segal

Proc. Amer. Math. Soc. 39 (1973), 625-628

DOI: https://doi.org/10.1090/S0002-9939-1973-0368041-4

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Abstract:

The peculiar properties of the ${2^j} - 2$ dimensional generators of unitary bordism (the $2$-primary Milnor generators) are related to the ${2^j} - 3$ dimensional indecomposable torsion classes of Alexander. This result is then used to confirm a conjecture of Ray concerning the generalised homology spectral sequence for $MS{p_\ast }(MU)$. Finally it is noted that Ray’s conjecture to the effect that all classes in $MS{p_\ast }$ are detectable by KO-characteristic numbers must fail.

References

J. C. Alexander, A family of indecomposable symplectic manifolds, Amer. J. Math. 94 (1972), 699–710. MR 310914, DOI 10.2307/2373752
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
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
Nigel Ray, Some results in generalized homology, $K$-theory and bordism, Proc. Cambridge Philos. Soc. 71 (1972), 283–300. MR 290383, DOI 10.1017/s0305004100050520
D. M. Segal, On the symplectic cobordism ring, Comment. Math. Helv. 45 (1970), 159–169. MR 263094, DOI 10.1007/BF02567323
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