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The symplectic bordism ring

Published online by Cambridge University Press:  24 October 2008

Nigel Ray
Nigel Ray
Affiliation:
University of Manchester
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Extract

This paper is concerned with the symplectic bordism ring MSp*, whose structure is still largely unknown despite the partial results of Liulevicius(3), Novikov(4) and Stong(lO). It is the first of two elaborating(8), and it relies completely on (7) for notation and prerequisites. In particular we assume the reader to be familiar with (7), section 8, which establishes the relation between the Sp Hattori-Stong conjecture (that KO decides MSp) and the spectral sequence

We are here concerned entirely with computations in this spectral sequence.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 71 , Issue 2 , March 1972 , pp. 271 - 282
Copyright
Copyright © Cambridge Philosophical Society 1972

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References

REFERENCES

(1)Adams, J. F.S. P. Novikov's work on operations on complex cobordism. Mimeo. notes (University of Chicago, 1967).Google Scholar
(2)Brown, E. H. and Petersen, F. P.A spectrum whose ZP cohomology is the algebra of reduced pth powers. Topology 5 (1966), 149–154.CrossRefGoogle Scholar
(3)Liulevicius, A.Notes on the homotopy of Thorn spectra. Amer. J. Math. 86 (1964), 1–16.CrossRefGoogle Scholar
(4)Novikov, S. P.Homotopy properties of Thom complexes. Math. Sb. 57 (1962), 407–442. (Russian.)Google Scholar
(5)Ray, N. Ph.D. Thesis, University of Manchester (1969).Google Scholar
(6)Ray, N.Realizing symplectic bordism classes. Proc. Cambridge Philos. Soc. 71 (1972), 301–305.CrossRefGoogle Scholar
(7)Ray, N.Some results in generalized homology, K-theory and bordism. Proc. Cambridge Philos. Soc. 71 (1972), 283–300.CrossRefGoogle Scholar
(8)Ray, N.Anote on the symplectic bordism ring. Bull. London Math. Soc. 3 (1971), 159–162.CrossRefGoogle Scholar
(9)Ray, N. and Switzer, R. M.On SU × SU bordism. Quart. J. Oxford Series (2) 21 (1970), 137–150.CrossRefGoogle Scholar
(10)Stong, R. E.Some remarks on symplectic cobordism. Ann. of Math. 86 (1967), 425–433.CrossRefGoogle Scholar
(11)Stong, R. E.Notes on cobordism theory (Princeton University Press, 1968).Google Scholar