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Proceedings of the American Mathematical Society

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



Halving the Milnor manifolds and some conjectures of Ray

Author: David M. Segal
Journal: Proc. Amer. Math. Soc. 39 (1973), 625-628
MSC: Primary 57D90
MathSciNet review: 0368041
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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.

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Keywords: Unitary bordism, symplectic bordism, Milnor manifolds, Hattori-Stong conjecture
Article copyright: © Copyright 1973 American Mathematical Society