Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-25T06:19:48.829Z Has data issue: false hasContentIssue false
  • English
  • Français

Frame Fields on Manifolds

Published online by Cambridge University Press:  20 November 2018

Tze Beng Ng
Tze Beng Ng*
Affiliation:
National University of Singapore, Kent Ridge, Singapore
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Consider the following stable secondary cohomology operations associated with the relations in the mod 2 Steenrod algebra:

such that

Let ψ5 be a stable tertiary cohomology operation associated with the above relation. We assume that (ϕ4, ϕ5) and ψ5 are chosen to be spin trivial in the sense of Theorem 3.7 of [14].

Let ϕ0,0, ϕ1,1 be the stable Adams basic secondary cohomology operations associated with the relations:

respectively.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 1 , 01 February 1986 , pp. 232 - 256
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Adém, J. and Gitler, S., Secondary characteristic classes and the immersion problem, Bol. Soc. Mat. Mex. 8 (1963), 53–78.Google Scholar
2. Atiyah, M. F., Thorn complexes, Proc. London Math. Soc. 11 (1961), 291–310.Google Scholar
3. Gilter, S. and Mahowald, M. E., The geometric dimension of real stable vector bundles, Bol. Soc. Mat. Mex. 11 (1960), 85–106.Google Scholar
4. Hughes, A. and Thomas, E., A note on certain secondary cohomology operations, Bol. Soc. Mat. Mex. 13 (1968), 1–17.Google Scholar
5. Mahowald, M. E., The index of a tangent 2-field, Pacific Journal of Maths. 58 (1975), 539–548.Google Scholar
6. Maunder, C. R. F., Cohomology operations of the N-th kind, Proc. London Math. Soc. (1960), 125–154.Google Scholar
7. Milgram, J., Cartan formulae, Ill. J. of Math. 75 (1971), 633–647.Google Scholar
8. Beng, Tze Ng, The existence of 7-fields and 8-fields on manifolds, Quart. J. Math Oxford 30 (1979), 197–221.Google Scholar
9. Beng, Tze Ng, The mod 2 cohomology of BŜOn〈16〉, to appear in Can. J. Math.Google Scholar
10. Beng, Tze Ng, Fourth order cohomology operations and the existence of 9-fields on manifolds, to appear.Google Scholar
11. Quillen, D. G., The mod 2 cohomology rings of extra-special 2-groups and the spinor groups. Math. Ann. 194 (1971), 197–211 Google Scholar
12. Randall, D., Tangent frame fields on spin manifolds, Pacific Journal of Mathematics 76 (1978), 157–167.Google Scholar
13. Thomas, E., Postnikov invariants and higher order cohomology operations, Ann. of Math. 85 (1967), 184–217.Google Scholar
14. Thomas, E., Real and complex vector fields on manifolds, J. Math, and Mechanic. 16 (1967), 1183–1205.Google Scholar
15. Thomas, E., The index of a tangent 2-fields, Comment. Math. Helv. 42 (1967), 86–110.Google Scholar
16. Thomas, E., The span of a manifold, Quart. J. Math. 19 (1968), 225–244.Google Scholar
17. Thomas, E., Steenrood square and H-space, Ann. of Math. 77 (1963), 306–317.Google Scholar