Fibrations and homotopy type
HTML articles powered by AMS MathViewer
- by J. L. Noakes
- Proc. Amer. Math. Soc. 90 (1984), 619-630
- DOI: https://doi.org/10.1090/S0002-9939-1984-0733417-7
- PDF | Request permission
Abstract:
We prove the results announced in [13]. These allow us to distinguish homotopy types of spherical fibrations using fibre homotopy invariants.References
- A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573
- Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223β255. MR 155330, DOI 10.2307/1970341
- Peter Hilton and Joseph Roitberg, On principal $S^{3}$-bundles over spheres, Ann. of Math. (2) 90 (1969), 91β107. MR 246320, DOI 10.2307/1970683
- S. Y. Husseini, Spherical fibrations, The Steenrod Algebra and its Applications (Proc. Conf. to Celebrate N. E. Steenrodβs Sixtieth Birthday, Battelle Memorial Inst., Columbus, Ohio, 1970) Lecture Notes in Mathematics, Vol. 168, Springer, Berlin, 1970, pp.Β 107β124. MR 0278307
- I. M. James, On the suspension sequence, Ann. of Math. (2) 65 (1957), 74β107. MR 83124, DOI 10.2307/1969666
- I. M. James, Which fibre spaces are decomposable?, Indag. Math. 37 (1975), no.Β 5, 385β390. Nederl. Akad. Wetensch. Proc. Ser. A 78. MR 0388393
- I. M. James and J. H. C. Whitehead, Note on fibre spaces, Proc. London Math. Soc. (3) 4 (1954), 129β137. MR 61837, DOI 10.1112/plms/s3-4.1.129 β, The homotopy theory of sphere bundles over spheres, Proc. London Math. Soc. 3 (1954), 196-218.
- I. M. James and J. H. C. Whitehead, The homotopy theory of sphere bundles over spheres. II, Proc. London Math. Soc. (3) 5 (1955), 148β166. MR 68836, DOI 10.1112/plms/s3-5.2.148
- W. S. Massey, On the cohomology ring of a sphere bundle, J. Math. Mech. 7 (1958), 265-289. MR 0093763, DOI 10.1512/iumj.1958.7.57020
- John W. Milnor and James D. Stasheff, Characteristic classes, Annals of Mathematics Studies, No. 76, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974. MR 0440554
- Guido Mislin, The genus of an $H$-space, Symposium on Algebraic Topology (Battelle Seattle Res. Center, Seattle, Wash., 1971) Lecture Notes in Math., Vol. 249, Springer, Berlin, 1971, pp.Β 75β83. MR 0339149
- J. L. Noakes, Spherical fibrations, Bull. Amer. Math. Soc. (N.S.) 3 (1980), no.Β 2, 853β856. MR 578378, DOI 10.1090/S0273-0979-1980-14829-6
- J. L. Noakes, Self-maps of sphere bundles. I, J. Pure Appl. Algebra 10 (1977/78), no.Β 1, 95β99. MR 464235, DOI 10.1016/0022-4049(77)90031-7
- J. L. Noakes, Unstable $J$-invariants, Quart. J. Math. Oxford Ser. (2) 27 (1976), no.Β 105, 51β57. MR 394656, DOI 10.1093/qmath/27.1.51
- J. L. Noakes, Flows on fibre bundles, Trans. Amer. Math. Soc. 259 (1980), no.Β 2, 629β635. MR 567102, DOI 10.1090/S0002-9947-1980-0567102-2
- James Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239β246. MR 154286, DOI 10.1016/0040-9383(63)90006-5
- George W. Whitehead, On products in homotopy groups, Ann. of Math. (2) 47 (1946), 460β475. MR 0016672, DOI 10.2307/1969085
- George W. Whitehead, A generalization of the Hopf invariant, Ann. of Math. (2) 51 (1950), 192β237. MR 41435, DOI 10.2307/1969506
Bibliographic Information
- © Copyright 1984 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 90 (1984), 619-630
- MSC: Primary 55R05; Secondary 55P10, 55P60, 55R10
- DOI: https://doi.org/10.1090/S0002-9939-1984-0733417-7
- MathSciNet review: 733417