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A note on immersing manifolds in euclidean spaces

Published online by Cambridge University Press:  17 April 2009

Ng Tze Beng
Ng Tze Beng
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 0511
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Abstract

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Let M be a closed, connected smooth and 3-connected mod 2 (that is Hi(M;ℤ2) = 0, 0 < i ≤ 3) manifold of dimension n = 7 + 8k. Using a combination of cohomology operations on certain cohomology classes of M and on the Thom class of the stable normal bundle of M we show that under certain conditions M immerses in R2n−8. This extends previously known results for such a general manifold when the number of 1's in the dyadic expansion of n is less than 8.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 36 , Issue 2 , October 1987 , pp. 215 - 226
Copyright
Copyright © Australian Mathematical Society 1987

References

[1]Adém, J. and Gitler, S., Secondary characteristic classes and the immersion problem”, Bol. Soc. Mat. Mexicana, 8 (1963), 53–78.Google Scholar
[2]Atiyah, M.F., “Thom complexes”, Proc. London Math. Soc. (3) 11 (1961), 29–310.Google Scholar
[3]Gitler, S. and Mahowald, M.E., “The geometric dimension of real stable vector bundles”, Bol. Soc. Mat. Mexicana, 11 (1960), 85–106.Google Scholar
[4]Hirsch, M.W., “'Immersion of manifolds”, Trans. Amer. Math. Soc. 93 (1959), 242–276.CrossRefGoogle Scholar
[5]Massey, W.S. and Peterson, F.P., “On the dual Stiefel-Whitney classes of a manifolds:, Bol. Soc. Mat. Mexicana (2) 8 (1963), 1–13.Google Scholar
[6]Ng, Tze-Beng, “The existence of 7-fields and 8-fields on manifolds”, Quart. J. Math. Oxford Ser. (2) 30 (1979), 197–221.CrossRefGoogle Scholar
[7]Ng, Tze-Beng, “Frame fields on manifolds”, Canad. J. Math. 38 (1986), 232–256.CrossRefGoogle Scholar
[8]Ng, Tze-Beng, “Vector bundles over (8k+3) – dimensional manifo1ds”, Pacific J. Math. vol. 121 (1986), 427–443.CrossRefGoogle Scholar
[9]Quillen, D., “The mod 2 cohomology rings of extra-special 2-groups and the spinor groups”, Math. Ann. 194 (1971), 197–212.CrossRefGoogle Scholar
[10]Randall, D., “Some immersion theorems for manifolds”, Trans. Amer. Math. Soc. 156 (1971), 45–58.CrossRefGoogle Scholar
[11]Thomas, E., “Postnikov inveriants and higher order cohomology operations”, Ann. of Math. (2) 85 (1967), 184–217.CrossRefGoogle Scholar
[12]Thomas, E., “Real and complex vector fields on manifolds”, J. Math. Mech. 16 (1967), 1183–1205.Google Scholar
[13]Thomas, E., “The span of a manifold”, Quart. J. Math Oxford Ser. (2) 19 (1968), 225–244.CrossRefGoogle Scholar