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References
Adams, J.F.: On the groupsJ(X), II. Topology3, 137–171 (1965)
Araki, S.: Typical formal groups in complex cobordism andK-theory. (Lecture notes in Math.) Kyoto Univ. (1973)
Atiyah, M.F., Rees, E.: Vector bundles on Projective 3-Space. Invent. Math.35, 131–153 (1976)
Atiyah, M.F., Smith, L.: Compact Lie groups and the stable homotopy of spheres. Topology13, 135–142 (1974)
Atiyah, M.F., Todd, J.A.: On complex Stiefel manifolds. Proc. Camb. Phil. Soc.56, 342–353 (1960)
Crabb, M.C.: ℤ/2-Homotopy Theory. London Math. Soc. Lecture Note Series, Vol. 44. Cambridge University Press 1980
Crabb, M.C.: Desuspension of the image ofJ (preprint)
Crabb, M.C.: On theKO ℤ/2-Euler class (preprint)
Crabb, M.C., Knapp, K.: Adams periodicity in stable homotopy. Topology24, 475–486 (1985)
Crabb, M.C., Knapp, K.: Vector bundles of maximal codegree. Math. Z.193, 285–296 (1986)
Crabb, M.C., Knapp, K.: The Hurewicz map on stunded complex projective spaces. Am. J. Math. (in press)
Crabb, M.C., Knapp, K.: James quasi-periodicity for the codegree of vector bundles over complex projective spaces. J. London Math. Soc.35, 353–366 (1987)
Crabb, M.C., Knapp, K.: On the codegree of negative multiples of the Hopf bundle. Proc. R. Soc. Edinb.107, 87–107 (1987)
Crabb, M.C., Knapp, K.: Adams trivialization, Im(J)-theory and the codegree of vector bundles (in preparation)
Crabb, M.C., Sutherland, W.A.: A bundle over the tangent sphere-bundle of a π-manifold. Q. J. Math. Oxford30, 1–19 (1979)
Crabb, M.C., Sutherland, W.A.: The space of sections of a sphere-bundleI. Proc. Edinb. Math. Soc.29, 383–403 (1986)
Deninger, Ch., Singhof, W.: Thee-invariant and the spectrum of the Laplacian for compact nilmanifolds covered by Heisenberg groups. Invent. Math.78, 101–112 (1984)
Fujii, M.:KO-groups of projective spaces. Osaka J. Math.4, 141–149 (1967)
Garcia, A.: Sobre el orden del mapeo de pegue de las caldes en ℂP n+k n . Bol. Soc. Mat. Mex25, 53–57 (1980)
Gray, B.: On the sphere of origin of infinite families in the homotopy groups of spheres. Topology8, 219–232 (1969)
Iriye, K.: On the James number of cyclic maps of spheres. Japan J. Math.10, (No. 1) 1–8 (1984)
James, I.M.: The topology of Stiefel manifolds. London Math. Soc. Lecture Note Series, Vol. 24. Cambridge University Press 1976
James, I.M.: Cross-sections of Stiefel manifolds. Proc. London Math. Soc.8, 536–547 (1958)
Löffler, P., Smith, L.: Line bundles over framed manifolds. Math. Z.138, 35–52 (1974)
Malyî, B.D.: Euler classes of stably equivalent vector bundles. Izv. Akad. Nauk SSSR. Ser. Math.38, 113–131 (1974)
May, J.P., Milgram, R.J.: The Bockstein and the Adams spectral sequence. Proc. Am. Math. Soc.83, 128–130 (1981)
Ōshima, H.: On the stable James numbers of complex projective spaces. Osaka J. Math.11, 361–366 (1974)
Ōshima, H.: Some James numbers of Stiefel manifolds. Math. Proc. Camb. Phil. Soc.92 139–161 (1982)
Roush, F.W.: Transfer in generalized cohomology theories. Dissertation, Princeton 1971
Sigrist, F., Suter, U.: On immersions ℂP n→ℝ4n-2α(n). Lecture Notes Math., Vol. 673, 106–115 Berlin, Heidelberg, New York: Springer 1978
Ucci, J.: Symmetric maps of spheres of least positive James number. Indiana Univ. Math. J.21, 709–714 (1972)
Walker, G.: Estimates for the complex and quaternionic James numbers. Q. J. Math. Oxford32, 467–489 (1981)
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Crabb, M.C., Knapp, K. James numbers. Math. Ann. 282, 395–422 (1988). https://doi.org/10.1007/BF01460042
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DOI: https://doi.org/10.1007/BF01460042